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

1 Answer
Jan 9, 2016

Answer:

#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#