Number Patterns and Sequences

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

​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!

​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

​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, ...

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