Q12 of 104 Page 488

The sum of an infinite geometric series is 20, and the sum of the squares of these terms is 100. Find the series.

Given: &


(because on squaring both first term a and common ratio r will be squared.)


To find: the series


a=20(1-r)…(i)


⇒ …(from (i))


⇒


⇒ 100(1+r)=400(1-r)


⇒ 100+100r=400-400r


⇒ 100r+400r=400-100


⇒ 500r=300


⇒ 5r=3


⇒


Put this value of r in equation (i) we get



∴The infinite geometric series is:8,


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