M1W1 Generating Patterns (sequence and patterns)

GENERATING
PATTERNS
MATHEMATICS 10 – MODULE 1
Prepared By: Chriza D. Suarez

OBJECTIVES
describes and
generates
patterns
find the next
term of a
sequence.
finds the
general term
or nth term of
a sequence
M1: GENERATING PATTERNS

CAN YOU SPOTTHE PATTERN?
Identify what comes next in the pattern of figures or list of numbers.
60
1,280
7.5

LESSON 2
SEQUENCE
PATTERN is also known as a SEQUENCE.
is an arrangement of elements or numbers
that usually follow a particular rule. It can be
finite (elements can be counted) or infinite
(the pattern goes on).

 FINITE SEQUENCE (can be counted)
example: 0, 3, 6, 9, 12, 15
This sequence has exactly 6
elements
 INFINITE SEQUENCE (cannot be
counted)
example: 10, 20, 30, 40 …
Three dots mean it keeps going

Can you give an example of a finite
sequence?

Can you give an example of an infinite
sequence?

SEQUENCE
is a set of numbers written in a specific order:
, …
Each element in a sequence is called a TERM. It can be
represented by using where n is the position of the term.
Ex. 1: 0, 3, 6, 9, 12, 15
The first term is 0, the second term is 3, the third
term is 6, = 9 and = 12.
Ex. 2: 0, 20, 30, 40 …
= 10, = 20, = 30, = 40, etc.

SEQUENCE

LET’S APPLY
29 35 41 Add 6
-56-112-224 Multiply to
2
*
*

FINDINGTHE NEXTTERM OF A
SEQUENCE GIVEN ITS GENERALTERM
GENERAL TERM OR NTH TERM RULE is used to
generate and continue the sequence.
Example: Find the first 5 terms of the sequence given the general term:
.
Given:
The general term: = n + 3
Solution: First term: = 1 + 3 = 4
Second term = 2 + 3 = 5
Third term = 3 + 3 = 6
Fourth Term = 4 + 3 = 7
Fifth Term = 5 + 3 = 8
The first five terms of the sequence are 4, 5, 6, 7, 8.

Example: Ex. 4 Find the next three terms of where the first term is
5.
Given:
General term:
First term:
Solution:
Second term = 7(2) – 2 = 12
Third term = 7(3) – 2 = 19
Fourth Term = 7(4) – 2 = 26
The next three terms of the sequence are 12,
19 and 26.

LET’S APPLY
Sol #1
= 2+1
*
* 3
Sol #4
𝟓
𝟕

FINDINGTHE GENERALTERM OF A
SEQUENCE

FINDINGTHE GENERALTERM OF A
SEQUENCE
Example: Find the general term of the sequence: 2, 4, 6, 8, ….
Step 1: Write the given terms in a table.
Condition 1: It fits the given.
Answer: The general term of the sequence 2, 4, 6 8, ... is defined by the formula .
Step 2: Study the pattern rule.
Step 3: Check if the expression/formula, fits the given value by substitution.
Checking: If =2n ,
= 2(1) =2; = 2(3) =6
= 2(2) =4= 2(4) =8
Since we repeat adding 2 to each value of the
term, the short way to write this is by using
multiplication expression. That is .

FINDINGTHE GENERALTERM OF A SEQUENCE
Example: What is the 100th
term of the sequence 8, 13, 18, 23, . . . ?
Step 1: Write the given terms in a table.
Condition:
Step 2: Study the pattern rule.
Step 3: Check if the expression/formula, fits the given value by
substitution.

SEATWORK #2
Complete the table below by substituting the given values of
to and list down the terms of the sequence.
1 2 3 4 SEQUENCE
-2 1 4
3 6
-5
1

LESSON 2
SEQUENCE
- is a function, where the domain is a set
of consecutive positive integers beginning
with 1
GENERAL TERM OR NTH RULE
- is used t generate and continue the
sequence

Some of the function values, also known
as TERMS of the sequence are as follows:
,
,
,
The first term of the sequence is denoted
as , the fifth term as , and the nth term, or
general term as .

M1W1 Generating Patterns (sequence and patterns)

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