How can you determine the relationship between corresponding terms? Give an example.

You have to try to determine the sequence, and you try two basic kind of sequences: aritymethic and geometric.

In aritmetic sequeces the relationships is that the difference between any adjacent terms is constant.

For example

'Number of term (n) Term, An

1 7

2 11

3 15

4 19

Then the relationship between adjacent terms is 19 - 15 = 4 = 15 - 11 = 4 = 11 - 7 = 4.

You can find, then, a general expression that relates any term with its position.

It is An = 7 + (n-1) * 4

In geometric sequences the relationship is found dividing two adjacent terms, because the ratio is constant.

For example:

Number of term Term

1 10

2 20

3 40

4 80

You can then find the relation as: 20/10 = 2 = 40/20 = 2 = 80/40 = 2.

In this case the general term is An = 10 * 2^ (n-1)