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,