Question

The terms of a sequence are -2, -6, -10, -14, -18, what is the common difference, explicit and recursive formula?

Answer 1

The common difference is `-4`;

The explicit formula is `a_n=-2-4(n-1), n>0,ninNN`

The recursive formula is `a_1=-2 and a_(n+1)=a_n-4`

Explanation:

This is an arithmetic sequence. since you can find a common difference, that is

`-6-(-2)=-10-(-6)=-14-(-10)=-18-(-14)=-4`

The explicit formula is:

`a_n=-2-4(n-1), n>0,ninNN`

The recursive formula is:

`a_1=-2 and a_(n+1)=a_n-4`