If the sum of the infinite geometric progression is 18 and sum of the squares of the terms is 162. find the common ratio of the progression
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a,ar,ar^2, ar^3 , ar^4 ..................ar^n
sum of infinite GP is a/1-r
then
a/1-r = 18 ---------------(1)
a^2/1-r^2 = 162. ----------------(2)
eq. (1) a= 18- 18r put the eq.(2)
(18-18r)^2 / 1-r^2 = 162
(2-2r)^2/1-r^2=2
4(1-r)^2/1-r^2=2
2(1-r)(1-r)/(1-r)(1+r)=1
2(1-r)=(1+r)
2-2r=1+r
3r=1
r=1/3
sum of infinite GP is a/1-r
then
a/1-r = 18 ---------------(1)
a^2/1-r^2 = 162. ----------------(2)
eq. (1) a= 18- 18r put the eq.(2)
(18-18r)^2 / 1-r^2 = 162
(2-2r)^2/1-r^2=2
4(1-r)^2/1-r^2=2
2(1-r)(1-r)/(1-r)(1+r)=1
2(1-r)=(1+r)
2-2r=1+r
3r=1
r=1/3
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