In this worksheet, we will learn how to find the formula for the general term, **T _{n}**, of a sequence.

__Example__

Term no., n = 1 2 3 4 5

Term, T_{n}= 4 8 12 16 20

Common difference = +4 +4 +4 +4

It is clear, that** T _{n} = 4n**.

Also note that the difference between each term is 4.

Compare this sequence with the one below:

Term no., n = 1 2 3 4 5

Term, T_{n}= 7 11 15 19 23

Common difference = +4 +4 +4 +4

The common difference of **+4** tells us that this sequence is "related" to the first one .

It begins **T _{n} = 4n**... and so is in the

**4n**"family".

Compare the two and you will see that each term is **3** more than that in the first sequence.

7 = 4 + 3

11 = 8 + 3

15 = 12 + 3

So **T _{n} = 4n + 3 **