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) 

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