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,


1