SOLUTION: For a geometric sequence, the sum of the 4th and 5th terms is 144. The sum of the 2nd and 3rd terms is 16. Given that the common ratio is positive, determine the sum of the 6th ter

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Question 856913: For a geometric sequence, the sum of the 4th and 5th terms is 144. The sum of the 2nd and 3rd terms is 16. Given that the common ratio is positive, determine the sum of the 6th term.
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
Tn = t * r^(n - 1)
T4 = t * r^(n - 1)
T5 = t * r^(n - 1)
T4+T5=144
t * r^(3)+ t * r^(4)=144
T3 = t * r^(n - 1)
T2 = t * r^(n - 1)
T3+T2=16
t * r+ t * r^2=16,
t * r^(3)+ t * r^(4)=144
r = 3, t = 4/3
Your question is poorly worded.
Do you want just the 6th term or the sum of the first six terms?
r = 3, t = 4/3
Tn = t * r^(n - 1)
T6 = 4/3 * 3^(5)=324
The sixth term is 324
S=t*(1 - r^n)/(1 - r)
S=4/3*(1 - 3^6)/(1 - 3)
S=1456/3
S=485 1/3
The sum of the first six terms is 485 1/3