Question

10.) The sum of the 2nd and 3rd terms of a geometric series is 15. The sum of the 3rd and 4th terms is 60. Determine:

1) The ratio of the series
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b) The 8th term



(You get +10 points if your solution and answer is honest)

Answer 1

ar + ar^2 = 15
ar(1 + r) = 15

ar^2 + ar^3 = 60
ar^2(1 + r) = 60
divide the 2nd by the 1st equation:
ar^2(1 + r) / ( ar(1 + r) ) = 60/15
r = 4

back into the first:
ar(1 + r) = 15
4a(1+4) = 15
4a = 3
a = 3/4

check: our sequence is
3/4, 12/4, 48/4, 192/4, ....
3/4, 3, 12, 48, ...
sum of 2nd and 3rd = 3+12=15
sum of 3rd and 4th = 12+48 = 60

my answer is correct

curious: what do they mean by "answer is honest" ??

Answer 2

Good AM mathhelper! I highly appreciate your solution and answer. And to answer your question, I put that so people don't put answers that may not be related or using other questions as excuses like they didn't actually study. I'm currently in blended learning. Once again, thank you very much!