Question

What is the 7th term in the geometric sequence in which a10 is 9 and a13 is -72?

a. 2B. - 1/8C. - 9/8D. 1/4

Answer 1

recall, a geometric series has this form with constants A for n=0, and k, the ratio of two consecutive terms n/(n+1)

`a_n =A*k^n`

you are given two values, for n=13 and n=10, put both into the equation


`9=A*k^(10)`

`-72=A*k^(13)`


Two equations with two unknown values A and k, you can solve for those.

Solving both for A,

`A= (9)/(k^(10)) = (-72)/(k^(13))`



`k=-2`

`A= (9)/(1024)`

The general equation for the series is then,

`a_n= (9)/(1024)(-2)^n`

use n=7