Question

How do you find the explicit formula for the arithmetic sequence, then find `a_14` given `a_1=9, d=-5`?

Answer 1

`color(red)(a_14 = -56`

Explanation:

`a_1 = 9, d = -5`

`a_2 = a_1 + d = 9 - 5 = 4`

`a_3 = a_2 + d = a_1 + 2d = a_1 + (3-1) d = 4-5 = -1`

`:. a_n = a_1 + (n-1) * d` is the explicit formula.

`a_14 = a_1 + (14-1) * -5 = 9 - 65 = -56`