In a geometric series, t1=12 and S3=372. What is the greatest possible value for t5? Justify your answer.

Answer 1

The formula for the sum of n terms with a common ratio of r is
Sn=t1*(r^n-1)/(r-1)
In particular, S3=372, t1=12

(r^n-1)/(r-1)=S3/t1=31
=>
r=5, or r=-6

case r=5
t3=t1*r²=12*25=300

case r=-6
t3=t1*(-6)²=432

Make your choice of the answer and justify.