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

Question

1750 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-01-09T01:15:37

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

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