Question

The sum of terms of an infinite GP is 15. And the sum of the squares of the term is 45. Find the common ratio.​

Answer 1

a+ ar+ .......... = a)/ (1-r)

a^2 + (ar)^2+......

Now here common ratio is = r^2

first term = a^2

sum = a^2)/ ( 1- r^2).

a)/(1-r) = 15

a^2)/ (1-r^2)= 45

a^2)/ ( 1- r)( 1+r). = 45

a/(1-r) . a/(1+r) = 45

15 a/(1+r) = 45

a/(1+r)= 3

a/( 1-r)= 15

divide

1-r)/( 1+r)= 3/15= 1/5

5 - 5r = 1 + r

5-1 = r+5r

4 = 6r

r= 4/6 = 2/3

Common ratio is 2/3

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