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

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

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

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