Question

Can someone write an explicit formula for the following sequence for me?:

3, -4, -11, -18,... The d=-7.

Answer 1

`a_n=10-7n`

Explanation:

The explicit form for an arithmetic sequence is:

`a_n=a_1+d(n-1)`

where
`a_1` is the first term and [ted]d[/tex] is the common difference.

The given sequence is arithmetic because term-previous term is the same per each pair of term and previous term.

That is the following holds:

-4-3=-11-(-4)=-18-(-11)

All of these differences are equal to -7, the common difference.

So let's fill in the explicit form:

`a_n=3+-7(n-1)`

or

`a_n=3-7(n-1)`

or

`a_n=3-7n+7`

or

`a_n=10-7n`