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

__Example__

Term number n = 1 2 3 4 5

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

**The common difference is +4**

The common difference between the terms is **+4,** so we write this as **4n.**

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

Compare this sequence with the one below:

Term number n = 1 2 3 4 5

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

**The common difference is +4**

The common difference of **+4** gives us **4n **again.

But this time, we need to do something more.

If we test out 4n with the first term in the table, we get 4 x 1 = 4 but the first term **isn't 4**, it is actually **7**!

This means that we need to do an adjustment to the formula: 7 - 4 = 3, so we know that we need to **add 3** to the answer of 4n.

This gives us the corrected formula of **4n + 3**

To finish off, we need to test that formula out with some of the other terms to make sure it works:

n = 2 4 x 2 = 8 + 3 = 11, which is correct.

n = 3 4 x 3 = 12 + 3 = 15, which is also correct!

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

It's a bit tricky, but we'll take it step by step and work through the questions carefully.

Let's get started!