Question

Find the first four terms of the sequence defined by the explicit rule f(n)=7(n-1)-10. Is it an arithmetic sequence?

Answer 1

Yes

Explanation:

Explicit rules for arithmetic sequences follow the format `a_n=d(n-1)+a_1` (or with a `f(n)` instead of an `a_n`), where `d` represents the common difference and `a_1` represents the first term

To find the first 4 terms, plug `1, 2, 3, 4` in for `n`:

`f(1)=7(1-1)-10`

`f(1)=7(0)-10`

`f(1)=0-10`

`f(1)=-10`

Do the same thing for `2, 3, 4`

The first four terms are `-10, -3, 4, 11`