What is the 7th term of the geometric sequence where a1 = –4 and a5 = –1,024?

1 Answer
Nov 25, 2015

Answer:

#-16384# or #16384#

Explanation:

The common ratio #r# of this geometric sequence is a #4#th root of #(-1024)/(-4) = 256 = 4^4#, since #a_5 = r^4 a_1#

The possible Real #4#th roots are #+-4#

In either case:

#a_7 = r^2 a_5 = 16*(-1024) = -16384#

So why do I say that #a_7# may be #16384#?

The Complex numbers #+-4i# are also #4#th roots of #256#.

If #r = +-4i# then #r^2 = -16# and we find:

#a_7 = r^2 a_5 = (-16)*(-1024) = 16384#