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)
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" ??