A geometric progression containing 20 terms has 48 as its fifth term. The ratio of the sum of its first 6 terms to that of its first 3 terms is 9:1. Find the sum of its last 5 terms.
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Hello everyone.
I'm working on the following problem:
A geometric progression containing 20 terms has 48 as its fifth term. The ratio of the sum of its first 6 terms to that of its first 3 terms is 9:1. Find the sum of its last 5 terms.
Here's what I've done with it so far:
G.P.
n = 20
T_5 = 48 => a * r^4 = 48 . . . . . . (i)
S_6 : S_3 = 9 : 1
S_6 / S_3 = 9 / 1
S_6 = 9 * S_3
[ a * (1 - r^5) ] / (1 - r) = { [ a * (1 - r^3) ] / (1 - r) } * 9
1 - r^5 = 9 (1 - r^3) . . . . . . (ii)
At this point I'm stuck... can't seem to figure out a way to get a and r.
Once I have a and r the other part of the question is trivial.
Any help will be greatly appreciated.
Thanks,
Shahz.