SOLUTION: THE SUM OF AN INFINITE GEOMETRIC PROGRESSION IS 15 AND THE SUM OF THE SQUARES OF THESE TERMS IS 45. FIND THE SERIES.

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Question 941784: THE SUM OF AN INFINITE GEOMETRIC PROGRESSION IS 15 AND THE SUM OF THE SQUARES OF THESE TERMS IS 45. FIND THE SERIES.
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for sum of infinite GP is +a%2F%281-r%29
hence +a%2F%281-r%29+=15..........eq(1)

HE SUM OF THE SQUARES OF THESE TERMS IS 45
hence +a%5E2%2F%281-r%5E2%29+=45 ......eq(2)
divide eq(1) with eq (2)
+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%5E2%29%29%29+=15%2F45
+%28+a%2F%281-r%29%29%2F%28%28a%5E2%2F%281-r%29%281%2Br%29%29%29%29+=15%2F45
%281%2F1%29%2F%28a%2F%281%2Br%29+%29=1%2F3
%281%2Br%29%2Fa=1%2F3
a%2F%281%2Br%29+=3
move (1+r) to the right
+a=+%281%2Br%29%2A3
but from eq(1) +a%2F%281-r%29+=15
move (1-r) to the right
+a=+%281-r%29%2A15
from above expressions
%281%2Br%29%2A3++=+%281-r%29%2A15
3+3*r= 15*1-r*15
3+3r =15-15r
move -15r to the left
3+3r+15r =15
3+18r =15
18r =15-3
18r =12
r = +12%2F18
r= 2%2F3
but a = (1+r)*3
= %281%2B%282%2F3%29%29%2A3
=%28%283%2F3%29+%2B%282%2F3%29%29%2A3
= +%28%283%2B2%29%2F3+%29%2A3
= 5
a= 5, r= 2/3
series = 5, 10/3, 20/9,...