SlideShare a Scribd company logo
Investigate:1 1 1 3 5 9 17 31 57 105
a. Find the next three terms:
b. Write a mathematical sentence
which can be used as the formula in
finding the nth term of the sequence.
1 1 1 3 5 9 17 31 57 105 193 355 653
a. The next three terms are as
follows, 193 for the 11th term, 355 for
the 12th term, and 653 for the 13th term.
b. If we are going to investigate this
3
9
31
105
193
355
653
11th 12th 13th
5
17
57
sequence, we can observe that for each
number in the series (starting from the
value 3 [4th term] to last) is the sum of
preceding 3 numbers.
We can deduce that this is a Tribonacci
Sequence. The Tribonacci sequence
starts with three predetermined terms
and then each successive term is the
sum of the three preceding terms.
The table below shows the observation:
What to find (value) How to find
4th
term (3) 1st
+ 2nd
+ 3rd
terms (1+1+1)
5th
term (5) 2nd
+ 3rd
+ 4th
terms (1+1+3)
6th
term (9) 3rd
+ 4th
+ 5th
terms (1+3+5)
7th
term (17) 4th
+ 5th
+ 6th
terms (3+5+9)
In order to solve for the next three
terms (11th, 12th and 13th), we will make
use of this recurrence equation on
finding for the nth term where n ≥ 4:
Example, this is the formula if we want
to find the 4th term of a Tribonacci
sequence.
T4=T1+T2+T3 which comes from the
equation
Tn= Tn−3+ Tn−2+Tn−1 (the formula for
8th
term (31) 5th
+ 6th
+ 7th
terms (5+9+17)
9th
term(57) 6th
+ 7th
+8th
terms (9+17+31)
10th
term(105) 7th
+8th
+9th
terms (17+31+57)
11th
term (193) 8th
+9th
+ 10th
terms (31+57+105)
12th
term (355) 9th
+ 10th
+ 11th
terms (57+105+193)
13th
term (653) 10th
+11th
+12th
terms (105+193+355)
finding the nth term of a tribonacci
sequence)
3. For this kind of tile sequence, we can assert
that we can have different approach for solving the
nth figure. In our way, we used a function and
figures to solve this kind of problem.
First, we need to fill out each figures as a dimension
of square. To do this, let us name first the shown
sequence of tiles as figures
Visualizing the above sentence, here are the figures
formed:
Figure 1 Figure 2 Figure 3
2x2
dimension
3x3
dimension
4x4
dimension
Figure 4
Knowing that every nxn dimension are added by
1x1 dimension to arrive for the next figure, we can
conclude that the next figure would be a 6x6
dimension square. We can also explore from the
figures that in order to arrive at the dimension, we
can show it on mathematical expression (n+2)(n+2).
Say, for example, for figure 1, we noticed that we
5x5
dimension
don’t need to substitute any natural numbers to get
2x2 dimension for the first figure. Therefore, with a
view to get 2x2 dimension, we will just substitute
zero on the expression. (0+2)(0+2) will be simplified
to (2)(2) or 2x2 dimension. Now for the figure 2, we
noticed that the tiles are in 3x3 form, therefore, in
order to arrive for 3x3 dimension, we are going to
add 1 shift horizontally and 1 shift vertically which
then can be substituted to the expression which can
be seen as (1+2)(1+2) => (3)(3) or 3x3 dimension.
The pattern which can be noticed could be traced
for the next figures. Now, we can see that the tiles
without shades can be expressed into mathematical
expression 2(n+1), (n+1) tiles for the first column
and (n+1) tiles for the last column. To better
understand, we can visually show the expression
using the figures above. Say for example, for figure
3:
We arrived at the expression 2(n+1) to get the total
number of tiles which are not shaded by blue.
If we are going to construct a table for better
understanding, follow below.
n+1
2+1
3 non-shaded tiles
for first column n+1
2+1
3 non-shaded tiles
for last column
2(2+1) = 4+2 = 6 non-
shaded tiles
Now, going back to the problem letter a. How many
square tiles will it take to build the next figure?
Since we know that the predicted dimension of the
figure (which we’ll be calling figure 5) is 6x6. We can
tell that there are 4 shifts added vertically and
Figure Dimension Shift added
vertically
and
horizontally
(n)
Mathematical
expression
(n+2)(n+2)
Mathematical
expression
2(n+1)
1 2x2 0 shift /
No shift
(0+2)(0+2) 2(0+1)
2 3x3 1 shift (1+2)(1+2) 2(1+1)
3 4x4 2 shifts (2+2)(2+2) 2(2+1)
4 5x5 3 shifts (3+2)(3+2) 2(3+1)
5 6x6 4 shifts (4+2)(4+2) 2(4+1)Next figure
horizontally inferring to the figure 1 which can be
shown below.
Now in, order to find the the non-shaded
tiles, we will just substitute n=4 to 2(n+1) =>
2(4+1) = 10 non-shaded tiles.
Added shifts four
units horizontally
Added shifts four
units vertically
6x6 dimension square
This basically means that there are 5 non-
shaded tiles for top left column and 5 non-
shaded tiles for bottom right column of a 6x6
dimension which can be shown below.
We are asked to find the number of square
tiles (shaded tiles).
We can find the shaded tiles by inspection which is
26 shaded tiles. On the other side, we can also
figure out the number of the shaded tiles by making
a function shown below.
n+1
4+1
5 non-shaded tiles
for last column
n+1
4+1
5 non-shaded tiles
for first column
f(n) = (n+2)(n+2)-2(n+1)
where (n+2)(n+2) will be the
arrangement/dimension of the tiles and 2(n+1) are
tiles which are non-shaded.
Knowing that n=4, we can substitute it to the
function;
f(4) = (4+2)(4+2) – 2(4-1)
= (6)(6) – 2(5)
= 36 – 10
= 26
Therefore, we conclude that we can also get the
number of shaded tiles by using functions.
b. To get the number of tiles for an nth figure,
we will subtract 2(n+1) from (n+2)(n+2) which can
be shown as a function:
Solving by Function =
Solving by Inspection
26 = 26
TRUE
f(n) = (n+2)(n+2)-2(n+1)

More Related Content

What's hot

Union and intersection of events (math 10)
Union and intersection of events (math 10)Union and intersection of events (math 10)
Union and intersection of events (math 10)
Damone Odrale
 
Rational Expressions Module
Rational Expressions ModuleRational Expressions Module
Rational Expressions Module
Lorie Jane Letada
 
Mathematics 10 - Lesson 1: Number Pattern
Mathematics 10 - Lesson 1: Number PatternMathematics 10 - Lesson 1: Number Pattern
Mathematics 10 - Lesson 1: Number Pattern
Juan Miguel Palero
 
Statistics and probability lesson6&7
Statistics and probability lesson6&7Statistics and probability lesson6&7
Statistics and probability lesson6&7
MARIA CHRISTITA POLINAG
 
Finite Geometric Series dlp
Finite Geometric Series dlpFinite Geometric Series dlp
Finite Geometric Series dlp
Richard Paulino
 
Evaluating Rational Algebraic Expressions
Evaluating Rational Algebraic ExpressionsEvaluating Rational Algebraic Expressions
Evaluating Rational Algebraic Expressions
Lorie Jane Letada
 
Measures of position
Measures of positionMeasures of position
Measures of position
Erlyn Geronimo
 
1st Mathematics 7 Quiz Bee 2023.pptx
1st  Mathematics 7 Quiz Bee 2023.pptx1st  Mathematics 7 Quiz Bee 2023.pptx
1st Mathematics 7 Quiz Bee 2023.pptx
AvilosErgelaKram
 
DLL_WEEK3_LC39-40.docx
DLL_WEEK3_LC39-40.docxDLL_WEEK3_LC39-40.docx
DLL_WEEK3_LC39-40.docx
nestthecasidsid2
 
Arithmetic Sequence and Arithmetic Series
Arithmetic Sequence and Arithmetic SeriesArithmetic Sequence and Arithmetic Series
Arithmetic Sequence and Arithmetic Series
Joey Valdriz
 
Arithmetic Sequence
Arithmetic SequenceArithmetic Sequence
Arithmetic Sequence
jennytuazon01630
 
Math-Quiz-Bee.ppt
Math-Quiz-Bee.pptMath-Quiz-Bee.ppt
Math-Quiz-Bee.ppt
VivianPercela1
 
Strategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the rootsStrategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the roots
maricel mas
 
DECILE : MEASURES OF POSITION FOR GROUPED DATA
DECILE : MEASURES OF POSITION FOR GROUPED DATADECILE : MEASURES OF POSITION FOR GROUPED DATA
DECILE : MEASURES OF POSITION FOR GROUPED DATA
Chuckry Maunes
 
probabilityofsimpleandcompoundevents-190217133041.pptx
probabilityofsimpleandcompoundevents-190217133041.pptxprobabilityofsimpleandcompoundevents-190217133041.pptx
probabilityofsimpleandcompoundevents-190217133041.pptx
Felix Jones Banares
 
MEASURES OF POSITION GROUPED DATA.pptx
MEASURES OF POSITION GROUPED DATA.pptxMEASURES OF POSITION GROUPED DATA.pptx
MEASURES OF POSITION GROUPED DATA.pptx
GeraldCorrales
 
MEASURES OF POSITION
MEASURES OF POSITIONMEASURES OF POSITION
MEASURES OF POSITION
Hazel Charise Gonzales
 
Multiplying Rational Expressions
Multiplying Rational ExpressionsMultiplying Rational Expressions
Multiplying Rational Expressions
Lorie Jane Letada
 
Rewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept formRewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept form
JanetEsteban1
 
Deciles & Quartiles - Point Measures
Deciles & Quartiles - Point  MeasuresDeciles & Quartiles - Point  Measures
Deciles & Quartiles - Point Measures
SweetChareyLouMapind
 

What's hot (20)

Union and intersection of events (math 10)
Union and intersection of events (math 10)Union and intersection of events (math 10)
Union and intersection of events (math 10)
 
Rational Expressions Module
Rational Expressions ModuleRational Expressions Module
Rational Expressions Module
 
Mathematics 10 - Lesson 1: Number Pattern
Mathematics 10 - Lesson 1: Number PatternMathematics 10 - Lesson 1: Number Pattern
Mathematics 10 - Lesson 1: Number Pattern
 
Statistics and probability lesson6&7
Statistics and probability lesson6&7Statistics and probability lesson6&7
Statistics and probability lesson6&7
 
Finite Geometric Series dlp
Finite Geometric Series dlpFinite Geometric Series dlp
Finite Geometric Series dlp
 
Evaluating Rational Algebraic Expressions
Evaluating Rational Algebraic ExpressionsEvaluating Rational Algebraic Expressions
Evaluating Rational Algebraic Expressions
 
Measures of position
Measures of positionMeasures of position
Measures of position
 
1st Mathematics 7 Quiz Bee 2023.pptx
1st  Mathematics 7 Quiz Bee 2023.pptx1st  Mathematics 7 Quiz Bee 2023.pptx
1st Mathematics 7 Quiz Bee 2023.pptx
 
DLL_WEEK3_LC39-40.docx
DLL_WEEK3_LC39-40.docxDLL_WEEK3_LC39-40.docx
DLL_WEEK3_LC39-40.docx
 
Arithmetic Sequence and Arithmetic Series
Arithmetic Sequence and Arithmetic SeriesArithmetic Sequence and Arithmetic Series
Arithmetic Sequence and Arithmetic Series
 
Arithmetic Sequence
Arithmetic SequenceArithmetic Sequence
Arithmetic Sequence
 
Math-Quiz-Bee.ppt
Math-Quiz-Bee.pptMath-Quiz-Bee.ppt
Math-Quiz-Bee.ppt
 
Strategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the rootsStrategic intervention material discriminant and nature of the roots
Strategic intervention material discriminant and nature of the roots
 
DECILE : MEASURES OF POSITION FOR GROUPED DATA
DECILE : MEASURES OF POSITION FOR GROUPED DATADECILE : MEASURES OF POSITION FOR GROUPED DATA
DECILE : MEASURES OF POSITION FOR GROUPED DATA
 
probabilityofsimpleandcompoundevents-190217133041.pptx
probabilityofsimpleandcompoundevents-190217133041.pptxprobabilityofsimpleandcompoundevents-190217133041.pptx
probabilityofsimpleandcompoundevents-190217133041.pptx
 
MEASURES OF POSITION GROUPED DATA.pptx
MEASURES OF POSITION GROUPED DATA.pptxMEASURES OF POSITION GROUPED DATA.pptx
MEASURES OF POSITION GROUPED DATA.pptx
 
MEASURES OF POSITION
MEASURES OF POSITIONMEASURES OF POSITION
MEASURES OF POSITION
 
Multiplying Rational Expressions
Multiplying Rational ExpressionsMultiplying Rational Expressions
Multiplying Rational Expressions
 
Rewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept formRewriting Linear Equation from standard form to slope intercept form
Rewriting Linear Equation from standard form to slope intercept form
 
Deciles & Quartiles - Point Measures
Deciles & Quartiles - Point  MeasuresDeciles & Quartiles - Point  Measures
Deciles & Quartiles - Point Measures
 

Similar to Precalculus Performance Task

Math blocks
Math blocksMath blocks
Math blocks
navajomath
 
Chapter 3: Figurate Numbers
Chapter 3: Figurate NumbersChapter 3: Figurate Numbers
Chapter 3: Figurate Numbers
Nathan Trillo
 
Magic squares
Magic squaresMagic squares
Magic squares
Jhenny Marie Juayong
 
The complete book_of_number_system1
The complete book_of_number_system1The complete book_of_number_system1
The complete book_of_number_system1
abhi_abhi22
 
Nikhil number pattern formulas
Nikhil number pattern formulasNikhil number pattern formulas
Nikhil number pattern formulas
ecooperms
 
Chap 03 02
Chap 03 02Chap 03 02
Chap 03 02
Jutay Nicavera
 
Maths project
Maths projectMaths project
Maths project
karan saini
 
class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numbers
karan saini
 
Maths project
Maths projectMaths project
Maths project
karan saini
 
Maths project
Maths projectMaths project
Maths project
karan saini
 
Equations problems
Equations problemsEquations problems
Equations problems
Educación
 
Sequence function
Sequence functionSequence function
Sequence function
jennytuazon01630
 
Stability criterion of periodic oscillations in a (13)
Stability criterion of periodic oscillations in a (13)Stability criterion of periodic oscillations in a (13)
Stability criterion of periodic oscillations in a (13)
Alexander Decker
 
101 math short cuts [www.onlinebcs.com]
101 math short cuts [www.onlinebcs.com]101 math short cuts [www.onlinebcs.com]
101 math short cuts [www.onlinebcs.com]
Itmona
 
AufEx4_01_02.ppt
AufEx4_01_02.pptAufEx4_01_02.ppt
AufEx4_01_02.ppt
SherwinSangalang3
 
1 chap
1 chap1 chap
Easy maths
Easy mathsEasy maths
Easy maths
Senthil Kanth
 
Visualizing the pascal’s triangle
Visualizing the pascal’s triangleVisualizing the pascal’s triangle
Visualizing the pascal’s triangle
Parth Dhar
 
Junior olympiad
Junior olympiadJunior olympiad
Junior olympiad
Mansyur Eppe
 
Geo chapter01power point
Geo chapter01power pointGeo chapter01power point
Geo chapter01power point
Huron School District
 

Similar to Precalculus Performance Task (20)

Math blocks
Math blocksMath blocks
Math blocks
 
Chapter 3: Figurate Numbers
Chapter 3: Figurate NumbersChapter 3: Figurate Numbers
Chapter 3: Figurate Numbers
 
Magic squares
Magic squaresMagic squares
Magic squares
 
The complete book_of_number_system1
The complete book_of_number_system1The complete book_of_number_system1
The complete book_of_number_system1
 
Nikhil number pattern formulas
Nikhil number pattern formulasNikhil number pattern formulas
Nikhil number pattern formulas
 
Chap 03 02
Chap 03 02Chap 03 02
Chap 03 02
 
Maths project
Maths projectMaths project
Maths project
 
class 10 chapter 1- real numbers
class 10 chapter 1- real numbersclass 10 chapter 1- real numbers
class 10 chapter 1- real numbers
 
Maths project
Maths projectMaths project
Maths project
 
Maths project
Maths projectMaths project
Maths project
 
Equations problems
Equations problemsEquations problems
Equations problems
 
Sequence function
Sequence functionSequence function
Sequence function
 
Stability criterion of periodic oscillations in a (13)
Stability criterion of periodic oscillations in a (13)Stability criterion of periodic oscillations in a (13)
Stability criterion of periodic oscillations in a (13)
 
101 math short cuts [www.onlinebcs.com]
101 math short cuts [www.onlinebcs.com]101 math short cuts [www.onlinebcs.com]
101 math short cuts [www.onlinebcs.com]
 
AufEx4_01_02.ppt
AufEx4_01_02.pptAufEx4_01_02.ppt
AufEx4_01_02.ppt
 
1 chap
1 chap1 chap
1 chap
 
Easy maths
Easy mathsEasy maths
Easy maths
 
Visualizing the pascal’s triangle
Visualizing the pascal’s triangleVisualizing the pascal’s triangle
Visualizing the pascal’s triangle
 
Junior olympiad
Junior olympiadJunior olympiad
Junior olympiad
 
Geo chapter01power point
Geo chapter01power pointGeo chapter01power point
Geo chapter01power point
 

More from paulangelomacaraeg

Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
paulangelomacaraeg
 
Module IV on PFA (Psychological First Aid) | Sources of Strengths
Module IV on PFA (Psychological First Aid) | Sources of StrengthsModule IV on PFA (Psychological First Aid) | Sources of Strengths
Module IV on PFA (Psychological First Aid) | Sources of Strengths
paulangelomacaraeg
 
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
paulangelomacaraeg
 
ELECTRONICS 10: VOLTAGE
ELECTRONICS 10: VOLTAGEELECTRONICS 10: VOLTAGE
ELECTRONICS 10: VOLTAGE
paulangelomacaraeg
 
ELECTRONICS 10: SERIES CIRCUIT
ELECTRONICS 10: SERIES CIRCUITELECTRONICS 10: SERIES CIRCUIT
ELECTRONICS 10: SERIES CIRCUIT
paulangelomacaraeg
 
ELECTRONICS 10: CURRENT QUIZ ANSWERS
ELECTRONICS 10: CURRENT QUIZ ANSWERSELECTRONICS 10: CURRENT QUIZ ANSWERS
ELECTRONICS 10: CURRENT QUIZ ANSWERS
paulangelomacaraeg
 
ELECTRONICS 10: CURRENT QUIZ
ELECTRONICS 10: CURRENT QUIZELECTRONICS 10: CURRENT QUIZ
ELECTRONICS 10: CURRENT QUIZ
paulangelomacaraeg
 
ELECTRONICS 10: PARALLEL CIRCUIT
ELECTRONICS 10: PARALLEL CIRCUITELECTRONICS 10: PARALLEL CIRCUIT
ELECTRONICS 10: PARALLEL CIRCUIT
paulangelomacaraeg
 
ELECTRONICS 10: RESISTANCE
ELECTRONICS 10: RESISTANCEELECTRONICS 10: RESISTANCE
ELECTRONICS 10: RESISTANCE
paulangelomacaraeg
 
ELECTRONICS 10: CURRENT
ELECTRONICS 10: CURRENTELECTRONICS 10: CURRENT
ELECTRONICS 10: CURRENT
paulangelomacaraeg
 
THE DECAMERON ENGLISH 10
THE DECAMERON ENGLISH 10THE DECAMERON ENGLISH 10
THE DECAMERON ENGLISH 10
paulangelomacaraeg
 
GRADE 10 UNIT TEST ENGLISH 3RD QUARTER
GRADE 10 UNIT TEST ENGLISH 3RD QUARTERGRADE 10 UNIT TEST ENGLISH 3RD QUARTER
GRADE 10 UNIT TEST ENGLISH 3RD QUARTER
paulangelomacaraeg
 
Contemporary Philippine Music
Contemporary Philippine MusicContemporary Philippine Music
Contemporary Philippine Music
paulangelomacaraeg
 

More from paulangelomacaraeg (13)

Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
Module II on PFA (Psychological First Aid) | Calming Down and Managing One’s ...
 
Module IV on PFA (Psychological First Aid) | Sources of Strengths
Module IV on PFA (Psychological First Aid) | Sources of StrengthsModule IV on PFA (Psychological First Aid) | Sources of Strengths
Module IV on PFA (Psychological First Aid) | Sources of Strengths
 
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
Module I on PFA (Psychological First Aid) | Validating Feelings and Normalizi...
 
ELECTRONICS 10: VOLTAGE
ELECTRONICS 10: VOLTAGEELECTRONICS 10: VOLTAGE
ELECTRONICS 10: VOLTAGE
 
ELECTRONICS 10: SERIES CIRCUIT
ELECTRONICS 10: SERIES CIRCUITELECTRONICS 10: SERIES CIRCUIT
ELECTRONICS 10: SERIES CIRCUIT
 
ELECTRONICS 10: CURRENT QUIZ ANSWERS
ELECTRONICS 10: CURRENT QUIZ ANSWERSELECTRONICS 10: CURRENT QUIZ ANSWERS
ELECTRONICS 10: CURRENT QUIZ ANSWERS
 
ELECTRONICS 10: CURRENT QUIZ
ELECTRONICS 10: CURRENT QUIZELECTRONICS 10: CURRENT QUIZ
ELECTRONICS 10: CURRENT QUIZ
 
ELECTRONICS 10: PARALLEL CIRCUIT
ELECTRONICS 10: PARALLEL CIRCUITELECTRONICS 10: PARALLEL CIRCUIT
ELECTRONICS 10: PARALLEL CIRCUIT
 
ELECTRONICS 10: RESISTANCE
ELECTRONICS 10: RESISTANCEELECTRONICS 10: RESISTANCE
ELECTRONICS 10: RESISTANCE
 
ELECTRONICS 10: CURRENT
ELECTRONICS 10: CURRENTELECTRONICS 10: CURRENT
ELECTRONICS 10: CURRENT
 
THE DECAMERON ENGLISH 10
THE DECAMERON ENGLISH 10THE DECAMERON ENGLISH 10
THE DECAMERON ENGLISH 10
 
GRADE 10 UNIT TEST ENGLISH 3RD QUARTER
GRADE 10 UNIT TEST ENGLISH 3RD QUARTERGRADE 10 UNIT TEST ENGLISH 3RD QUARTER
GRADE 10 UNIT TEST ENGLISH 3RD QUARTER
 
Contemporary Philippine Music
Contemporary Philippine MusicContemporary Philippine Music
Contemporary Philippine Music
 

Recently uploaded

How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
Celine George
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
zuzanka
 
220711130097 Tulip Samanta Concept of Information and Communication Technology
220711130097 Tulip Samanta Concept of Information and Communication Technology220711130097 Tulip Samanta Concept of Information and Communication Technology
220711130097 Tulip Samanta Concept of Information and Communication Technology
Kalna College
 
How to Manage Reception Report in Odoo 17
How to Manage Reception Report in Odoo 17How to Manage Reception Report in Odoo 17
How to Manage Reception Report in Odoo 17
Celine George
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
Nguyen Thanh Tu Collection
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
Prof. Dr. K. Adisesha
 
BPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end examBPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end exam
sonukumargpnirsadhan
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
indexPub
 
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
TechSoup
 
Information and Communication Technology in Education
Information and Communication Technology in EducationInformation and Communication Technology in Education
Information and Communication Technology in Education
MJDuyan
 
Observational Learning
Observational Learning Observational Learning
Observational Learning
sanamushtaq922
 
HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.
deepaannamalai16
 
Ch-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdfCh-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdf
lakshayrojroj
 
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر   أعد أحرف الخلاف سمير بسيوني.pdfمصحف القراءات العشر   أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
سمير بسيوني
 
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
andagarcia212
 
skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)
Mohammad Al-Dhahabi
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
danielkiash986
 
Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10
nitinpv4ai
 
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
Payaamvohra1
 
Oliver Asks for More by Charles Dickens (9)
Oliver Asks for More by Charles Dickens (9)Oliver Asks for More by Charles Dickens (9)
Oliver Asks for More by Charles Dickens (9)
nitinpv4ai
 

Recently uploaded (20)

How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17How to Download & Install Module From the Odoo App Store in Odoo 17
How to Download & Install Module From the Odoo App Store in Odoo 17
 
SWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptxSWOT analysis in the project Keeping the Memory @live.pptx
SWOT analysis in the project Keeping the Memory @live.pptx
 
220711130097 Tulip Samanta Concept of Information and Communication Technology
220711130097 Tulip Samanta Concept of Information and Communication Technology220711130097 Tulip Samanta Concept of Information and Communication Technology
220711130097 Tulip Samanta Concept of Information and Communication Technology
 
How to Manage Reception Report in Odoo 17
How to Manage Reception Report in Odoo 17How to Manage Reception Report in Odoo 17
How to Manage Reception Report in Odoo 17
 
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
CHUYÊN ĐỀ ÔN TẬP VÀ PHÁT TRIỂN CÂU HỎI TRONG ĐỀ MINH HỌA THI TỐT NGHIỆP THPT ...
 
Data Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsxData Structure using C by Dr. K Adisesha .ppsx
Data Structure using C by Dr. K Adisesha .ppsx
 
BPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end examBPSC-105 important questions for june term end exam
BPSC-105 important questions for june term end exam
 
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...
 
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
Elevate Your Nonprofit's Online Presence_ A Guide to Effective SEO Strategies...
 
Information and Communication Technology in Education
Information and Communication Technology in EducationInformation and Communication Technology in Education
Information and Communication Technology in Education
 
Observational Learning
Observational Learning Observational Learning
Observational Learning
 
HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.HYPERTENSION - SLIDE SHARE PRESENTATION.
HYPERTENSION - SLIDE SHARE PRESENTATION.
 
Ch-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdfCh-4 Forest Society and colonialism 2.pdf
Ch-4 Forest Society and colonialism 2.pdf
 
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر   أعد أحرف الخلاف سمير بسيوني.pdfمصحف القراءات العشر   أعد أحرف الخلاف سمير بسيوني.pdf
مصحف القراءات العشر أعد أحرف الخلاف سمير بسيوني.pdf
 
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
欧洲杯下注-欧洲杯下注押注官网-欧洲杯下注押注网站|【​网址​🎉ac44.net🎉​】
 
skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)skeleton System.pdf (skeleton system wow)
skeleton System.pdf (skeleton system wow)
 
Pharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brubPharmaceutics Pharmaceuticals best of brub
Pharmaceutics Pharmaceuticals best of brub
 
Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10Haunted Houses by H W Longfellow for class 10
Haunted Houses by H W Longfellow for class 10
 
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...
 
Oliver Asks for More by Charles Dickens (9)
Oliver Asks for More by Charles Dickens (9)Oliver Asks for More by Charles Dickens (9)
Oliver Asks for More by Charles Dickens (9)
 

Precalculus Performance Task

  • 1. Investigate:1 1 1 3 5 9 17 31 57 105 a. Find the next three terms: b. Write a mathematical sentence which can be used as the formula in finding the nth term of the sequence. 1 1 1 3 5 9 17 31 57 105 193 355 653 a. The next three terms are as follows, 193 for the 11th term, 355 for the 12th term, and 653 for the 13th term. b. If we are going to investigate this 3 9 31 105 193 355 653 11th 12th 13th 5 17 57
  • 2. sequence, we can observe that for each number in the series (starting from the value 3 [4th term] to last) is the sum of preceding 3 numbers. We can deduce that this is a Tribonacci Sequence. The Tribonacci sequence starts with three predetermined terms and then each successive term is the sum of the three preceding terms. The table below shows the observation: What to find (value) How to find 4th term (3) 1st + 2nd + 3rd terms (1+1+1) 5th term (5) 2nd + 3rd + 4th terms (1+1+3) 6th term (9) 3rd + 4th + 5th terms (1+3+5) 7th term (17) 4th + 5th + 6th terms (3+5+9)
  • 3. In order to solve for the next three terms (11th, 12th and 13th), we will make use of this recurrence equation on finding for the nth term where n ≥ 4: Example, this is the formula if we want to find the 4th term of a Tribonacci sequence. T4=T1+T2+T3 which comes from the equation Tn= Tn−3+ Tn−2+Tn−1 (the formula for 8th term (31) 5th + 6th + 7th terms (5+9+17) 9th term(57) 6th + 7th +8th terms (9+17+31) 10th term(105) 7th +8th +9th terms (17+31+57) 11th term (193) 8th +9th + 10th terms (31+57+105) 12th term (355) 9th + 10th + 11th terms (57+105+193) 13th term (653) 10th +11th +12th terms (105+193+355)
  • 4. finding the nth term of a tribonacci sequence)
  • 5. 3. For this kind of tile sequence, we can assert that we can have different approach for solving the nth figure. In our way, we used a function and figures to solve this kind of problem. First, we need to fill out each figures as a dimension of square. To do this, let us name first the shown sequence of tiles as figures Visualizing the above sentence, here are the figures formed: Figure 1 Figure 2 Figure 3 2x2 dimension 3x3 dimension 4x4 dimension
  • 6. Figure 4 Knowing that every nxn dimension are added by 1x1 dimension to arrive for the next figure, we can conclude that the next figure would be a 6x6 dimension square. We can also explore from the figures that in order to arrive at the dimension, we can show it on mathematical expression (n+2)(n+2). Say, for example, for figure 1, we noticed that we 5x5 dimension
  • 7. don’t need to substitute any natural numbers to get 2x2 dimension for the first figure. Therefore, with a view to get 2x2 dimension, we will just substitute zero on the expression. (0+2)(0+2) will be simplified to (2)(2) or 2x2 dimension. Now for the figure 2, we noticed that the tiles are in 3x3 form, therefore, in order to arrive for 3x3 dimension, we are going to add 1 shift horizontally and 1 shift vertically which then can be substituted to the expression which can be seen as (1+2)(1+2) => (3)(3) or 3x3 dimension. The pattern which can be noticed could be traced for the next figures. Now, we can see that the tiles without shades can be expressed into mathematical expression 2(n+1), (n+1) tiles for the first column and (n+1) tiles for the last column. To better understand, we can visually show the expression using the figures above. Say for example, for figure
  • 8. 3: We arrived at the expression 2(n+1) to get the total number of tiles which are not shaded by blue. If we are going to construct a table for better understanding, follow below. n+1 2+1 3 non-shaded tiles for first column n+1 2+1 3 non-shaded tiles for last column 2(2+1) = 4+2 = 6 non- shaded tiles
  • 9. Now, going back to the problem letter a. How many square tiles will it take to build the next figure? Since we know that the predicted dimension of the figure (which we’ll be calling figure 5) is 6x6. We can tell that there are 4 shifts added vertically and Figure Dimension Shift added vertically and horizontally (n) Mathematical expression (n+2)(n+2) Mathematical expression 2(n+1) 1 2x2 0 shift / No shift (0+2)(0+2) 2(0+1) 2 3x3 1 shift (1+2)(1+2) 2(1+1) 3 4x4 2 shifts (2+2)(2+2) 2(2+1) 4 5x5 3 shifts (3+2)(3+2) 2(3+1) 5 6x6 4 shifts (4+2)(4+2) 2(4+1)Next figure
  • 10. horizontally inferring to the figure 1 which can be shown below. Now in, order to find the the non-shaded tiles, we will just substitute n=4 to 2(n+1) => 2(4+1) = 10 non-shaded tiles. Added shifts four units horizontally Added shifts four units vertically 6x6 dimension square
  • 11. This basically means that there are 5 non- shaded tiles for top left column and 5 non- shaded tiles for bottom right column of a 6x6 dimension which can be shown below. We are asked to find the number of square tiles (shaded tiles). We can find the shaded tiles by inspection which is 26 shaded tiles. On the other side, we can also figure out the number of the shaded tiles by making a function shown below. n+1 4+1 5 non-shaded tiles for last column n+1 4+1 5 non-shaded tiles for first column
  • 12. f(n) = (n+2)(n+2)-2(n+1) where (n+2)(n+2) will be the arrangement/dimension of the tiles and 2(n+1) are tiles which are non-shaded. Knowing that n=4, we can substitute it to the function; f(4) = (4+2)(4+2) – 2(4-1) = (6)(6) – 2(5) = 36 – 10 = 26 Therefore, we conclude that we can also get the number of shaded tiles by using functions. b. To get the number of tiles for an nth figure, we will subtract 2(n+1) from (n+2)(n+2) which can be shown as a function: Solving by Function = Solving by Inspection 26 = 26 TRUE