Find the 110 term of the sequence - 7, 3, 13, 23, ...

First, find the nth term

To do this, find the term to term difference ...

A

-7 and 3 = 10

3 and 13 = 10

13 and 23 = 10

As the difference is 10, we now write out the 10 times table

10, 20, 30, 40

The next step is to work out how to get from the sequence to the 10x table

B

-7 - 10 = - 17

3 - 20 = - 17

13 - 30 = - 17

23 - 40 = - 17

Now use the answer from each section in the general formula

x = An + B

This could also be written as? n + ?

Using our numbers, this becomes 10n - 17

Now use the formula to work out the 110th term

(10 x 110) - 17

1100 - 17 = 1083