Number Patterns and Sequences

Number Patterns
Chapter 7.1

Objectives

1. Identify patterns in number sequences

2. Find a formula for the general term of a number sequence

3. Use the formula to find any term in a number sequence

Fill in the Blanks

What is the rule of the following sequence?

3, 8, 13, 18, 23, ...

Fill in the Blanks

Write down the next two terms of the sequence.

3, 8, 13, 18, 23, ...

Fill in the Blanks

What is the rule of the following sequence?

5, 15, 45, 135, 405, ...

Fill in the Blanks

Write down the next two terms of the following sequence.

5, 15, 45, 135, 405, ...

Word Cloud

Find the 238^th term of the following sequence.

10, 14, 18, 22, 26, ...

[you have 30 seconds only!]

​What do you notice from the previous question?

It is a slow process of continuous adding or subtraction to obtain the required term in a number sequence.

A simpler way is to determine the general term of a sequence!

General Term

​Number sequence	4,​	7,​	10,​	13,​	16,​	...​
​Position of each term n	​1	2​	3​	4​	5​	n

​1^st term

​2^nd term

​3^rd term

4^th term

5^th term

n^th term

​T₁

​T₂

T₃

T₄

T₅

T_n

Multiple Choice

80, 72, 64, 56, 48, ...

Which term is T₃ of the sequence?

• 80

• 72

• 64

• 56

Let's watch a video to see how to obtain the General Term

Let's try!

​5, 9, 13, 17, 21, ...

Work out the general term of the above sequence.

Difference = +4 4n

T₀ = 5 - 4
= 1

5, 9, 13, 17, 21, ...

​4n + 1

Fill in the Blanks

What is the general term of the following sequence?

7, 12, 17, 22, 27, ...

Multiple Choice

Which of the following is the general term of the sequence?

2, 8, 14, 20, 26, ...

• 6n + 6

• 6n - 6

• 6n + 4

• 6n - 4

Fill in the Blanks

Find the general term for the following sequence.

1, 4, 7, 10, 13, ...

Using General Term formula

T_n = 2n + 5

With the formula, we are able to find any term.

For example, 81^st term (T₈₁) = 2 (81) + 5 [substitute n = 81]
= 167

Multiple Choice

Given that T_n = 3n + 4,

find the 50^th term of the above sequence.

• 57

• 354

• 154

Fill in the Blanks

Back to the question: Find the 238^th term of the following sequence.

10, 14, 18, 22, 26, ...