SOLUTION: A GP has the second term as 9 and the fourth term as 81,find the sum of the list as the fourth term

Algebra ->  Sequences-and-series -> SOLUTION: A GP has the second term as 9 and the fourth term as 81,find the sum of the list as the fourth term      Log On


   

Question 1024168: A GP has the second term as 9 and the fourth term as 81,find the sum of the list as the fourth term
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
a%5B1%5D=a
a%5B2%5D=a%2Ar=9
a%5B3%5D=a%2Ar%5E2
a%5B4%5D=a%2Ar%5E3=81
So then,
%28a%2Ar%5E3%29%2F%28a%2Ar%29=81%2F9
r%5E2=9
r=3
and
a%2A3=9
a=3
I think you want the sum of the first 4 terms(?),

.
.
.
It could also be the case that,
r=-3 and then,
a%2A%28-3%29=9
a=-3
So then,
S=%28-3%29%281-3%2B9-27%29
S=60