# What is the 8th term of the geometric sequence where a1 = 625 and a3 = 25?

##### 1 Answer

Dec 20, 2015

It could be

#### Explanation:

The general term of this sequence is of the form:

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

where

Then:

#25 = a_3 = a r^2 = 625 r^2#

So

That results in two possibilities for

If

#a_8 = 625*(1/5)^7 = 5^(4-7) = 5^(-3) = 1/125#

If

#a_8 = 625*(-1/5)^7 = (-1)^7 5^(4-7) = -5^-3 = -1/125#