Question

2) Write a formula for the nth term of each arithmetic sequence. Then use the formula to find `a_15`?

b. `a_1=–3` and `d=6`

Answer 1

`a_n=6n-9` or `a_n=a_(n-1)+6`

`a_15=81`

Explanation:

To write an equation (explicit form, not recursive form) for an arithmetic sequence: `a_n=a_1+d(n-1)`, where `a_1` is the first term and `d` is the common difference. `n` is the term that we are trying to find (in this case, `a_15`).

Plug in `-3` and `6` for `a_1` and `d`, respectively

`a_n=-3+6(n-1)`

`a_n=-3+6n-6`

`a_n=6n-9 rarr` This is your equation in explicit form.

Let's solve for `a_15`:

`a_15=6*15-9`

`a_15=90-9`

`a_15=81`

Recursive form: `a_n=a_(n-1)+d rarr` To find `a_15`, you'd have to know the previous term (`a_14`).

Recursive form with `d` as `6`: `a_n=a_(n-1)+6`.