Question

A geometric sequence has a common ratio of 2 and the 12th term is −12,288.

What is the explicit rule that describes this sequence?

Answer 1

Explanation:

`\boxed {b_n=b_1q^(n-1)}`

`b_(12)=-12,288\ \ \ \ \ q=2\ \ \ \ n=12`

`-12,288=b_1(2^(12-1))\\\\-12,288=b_1(2^(11))\\\\-12,288=b_1(2048)`

Divide both parts of the equation by 2048:

`-0.006=b_1`

`Thus,\ b_1=-0.006`