Question

How do you find the explicit formula for the arithmetic sequence, then find `a_14` given `a_1=-4, d=17`?

Answer 1

`color(purple)(a_14 = a_1 + (14-1) * 17 = 217`

Explanation:

`a_1 = -4, d = 17`

`a_2 = a_1 + d = a_1 + (2-1) * d = -4 + 17 = 13`

`a_3 = a_2 + d = a_1 + (3-1) * d = -4 + 34 = 30`

`a_4 = a_3 + d = a_1 + (4-1) * d = -4 + 51 = 47`

`color(red)(a_n = a_(n-1) + d = a_1 + (n-1) * d`

`color(purple)(a_14 = a_1 + (14-1) * 17 = 217`