Question

What is the 9th term of the geometric sequence where a1 = -7 and a6 = -7,168?

Answer 1

`a_9 = -7 * 4^8 = -458752`

Explanation:

The general term of a geometric sequence can be written:

`a_n = a r^(n-1)`

where `a` is the initial term and `r` is the common ratio.

We are given:

`a = a_1 = -7`

`a r^5 = a_6 = -7168`

So `r = root(5)((-7168)/-7) = root(5)(1024) = root(5)(4^5) = 4`

(assuming we are dealing with a Real geometric sequence)

Then `a_9 = a r^8 = -7 * 4^8 = -7 * 65536 = -458752`