This document provides information about arithmetic sequences and series. It defines key terms like sequence, term, and common difference. It also presents methods for determining subsequent terms in a sequence, the nth term of a sequence using the explicit formula, finding arithmetic means between terms, and evaluating finite arithmetic series using the summation formula. Application examples are provided to demonstrate how to use these concepts to solve real-world problems involving sequences and series.
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
Geometric Series and Finding the Sum of Finite Geometric SequenceFree Math Powerpoints
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This powerpoint presentation discusses about the first lesson in Grade 10 Math. It is all about Number Pattern. It also shows the definition, examples and how to find the nth term and general formula.
Geometric Series and Finding the Sum of Finite Geometric SequenceFree Math Powerpoints
For more instructional resources, CLICK me here and DON'T FORGET TO SUBSCRIBE!
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Digital Tools and AI for Teaching Learning and Research
Notes 12.1 Arithmetic Sequences and Series.pdf
1. I. Sequences and Terms
• Sequence: a list of numbers
in a specific order.
1, 3, 4, 7, 10, 16
• Term: each number in a
sequence
Sequence
Terms
Notes 12.1: Arithmetic Sequences and Series
2. A sequence is arithmetic if the differences between consecutive terms are the
same.
4, 9, 14, 19, 24, . . .
9 – 4 = 5
14 – 9 = 5
19 – 14 = 5
24 – 19 = 5
arithmetic sequence
The common difference, d, is 5.
II. Arithmetic Sequences
FYI: Common differences
can be negative.
A. Definition
3. How do I know if it is an
arithmetic sequence?
• Look for a common difference between consecutive terms
Ex: 2, 4, 8, 16 . . . Common Difference?
2+2 = 4
4+ 4 = 8
8 + 8 = 16
No. The sequence is NOT Arithmetic
Ex: 48, 45, 42, 39 . . . Common Difference?
48 - 3 = 45
45 - 3 = 42
42 - 3 = 39
Yes. The sequence IS Arithmetic. d = -3
4. III. Finding Subsequent Terms
• Find the next three terms in
the arithmetic sequence:
2, 5, 8, 11, 14, __, __, __
• 2, 5, 8, 11, 14, 17, 20, 23
• The common difference is?
• 3!!!
5. IV. Finding the nth Term of an Arithmetic Sequence
an = a1 + (n - 1)d
Where:
an is the nth term in the
sequence
a1 is the first term
n is the number of the term
d is the common difference
6. Ex 1: Find the 25th term in the sequence of
5, 11, 17, 23, 29 . . .
an = a1 + (n - 1)d
a25 = 5 + (24)6 =149
Common difference
a2 - a1 = 11 – 5 = 6
a25 = 5 + (25 -1)6
Start with the explicit sequence formula
Find the common difference
between the values.
Substitute in known values
Simplify
7. Ex 2: Find the 17th term of the arithmetic
sequence: 26, 13, 0, -13
an = a1 + (n-1)d
a25 = 26 + (16)(-13) =-182
a25 = 26 + (17 -1)(-13)
Start with the explicit sequence formula
Find the common difference
between the values.
Plug in known values
Simplify
Common difference
a2 - a1 = 13 – 26 = -13
8. Ex 3: Find the first term of an arithmetic sequence if
the 9th term is 72 and the common difference is 5.
an = a1 + (n-1)d
72= a1 + (9-1)5
72= a1 + (8)5
72= a1 + 40
32= a1
9. Ex. 4: Suppose you have saved $75 towards the purchase of a new tablet. You
plan to save at least $12 from mowing your neighbor’s yard each week. In all,
what is the minimum amount of money you will have in 26 weeks?
an = a1 + (n-1)d
a26 = 75 + (26)12 =$387
difference = 12
a26 = 75 + (27 -1)12
Start with the explicit sequence formula
Find the common difference
between the values. You will save
$12 a week so this is your difference.
Substitute in known values
Simplify
WAIT: Why 27 and not 26 for n ?
The first term in the sequence, 75, came before the weeks started (think of it as week 0). Therefore you want one
more week in your formula to account for the $75 that you had before you started saving.
V. Application of Arithmetic Sequence
10. VI. Arithmetic Means
Arithmetic Means: the terms between any two
nonconsecutive terms of an arithmetic sequence.
Example: 17, 10, 3, -4, -11, -18, …
Between 10 and -18 there are three arithmetic means 3, -4, -11.
11. Ex 2: Find three arithmetic means between 8 and 14.
• So our sequence must look like 8, __, __, __, 14.
• In order to find the means we need to know the common
difference. We can use our formula to find it.
• 8, __, __, __, 14
• a1 = 8, a5 = 14, & n = 5
• 14 = 8 + d(5 - 1)
• 14 = 8 + d(4)
• 6 = 4d
• 1.5 = d
• 8, __, __, __, 14 so to find
our means we just add 1.5
starting with 8.
• 8, 9.5, 11, 12.5, 14
12. VII. Arithmetic Series
• A series is the expression for the sum of the terms of a sequence, not just
“what is the next term?”
Ex: 6, 9, 12, 15, 18 . .
.
This is a list of the numbers in the pattern an not a
sum. It is a sequence. Note it goes on forever, so we
say it is an infinite sequence.
Ex: 6 + 9 + 12 + 15 + 18
Note: if the numbers go on forever, it is infinite; if it has a
definitive ending it is finite.
Here we are adding the values. We call this a series.
Because it does not go on forever, we say it is a
finite series.
13. Sum of a Finite Arithmetic Series
)
(
2
1 n
n a
a
n
S
)
47
2
(
2
6
n
S
Where: Sn is the sum of all the terms
n = number of terms
a1 = first term
an = last term
For Example, 2 + 11 + 20 + 29 + 38 + 47 = 147
119
)
29
5
(
2
7
n
S
147
Let’s try one: evaluate the series: 5, 9, 13,17,21,25,29
14. • Ofelia sells houses in a new development. She makes a commission of
$3750 on the sale of her first house. For each additional house sold, her
commission increases by $500. Thus on her next house she will make
$4250. How many houses will she have to sell for her total commission to
be at least $65,000?
• In this situation, her commission is increasing by the same
amount each time, and we are asking for the sum of all her
commissions. Therefore, this represents an arithmetic series. We
are solving for n.
VIII. Application of Arithmetic Series
15. • Because we have two
unknowns (n and an ), we
need to substitute
something in for one of
them. We can substitute
• a1 + (n-1)d for an
)
(
2
1 n
n a
a
n
S
1 1
( ( ( 1) ))
2
n
n
S a a n d
1
(2 ( 1) )
2
n
n
S a n d
65000 (2(3750) ( 1)(500))
2
n
n
65000 (7500 500 500)
2
n
n
16. 65000 (7000 500 )
2
n
n
2
130000 7000 500
n n
2
0 500 7000 130000
n n
2
0 14 260
n n
n = 10.58; n=-24.58
She will need to sell 11 houses to make at lest $65,000 a year.