The sum of infinite number of terms in G.P. is 20 and the sum of their squares is 100. Then find the common ratio of G.P.

Explanation

`a+ar+ar^(2)+…`to`oo=20`
`rArra/(1-r)=20` (1)
`a^(2)+a^(2)r^(2)+a^(2)r^(4)+…`to `oo`=100
`rArra^(2)/(1-r^(2))=100` (2)
Squaring (1), we have
`a^(2)/((1-r)^(2))=400` (3)
Dividing (3) by (2), we get
`(a^(2)//(1-r^(2)))/(a^(2)//1-r^(2))=400/100`
or `(1-r^(2))/((1-r)^(2))=4`
or `(1+4)/(1-r)=4`
or 1+r=4-4r
or 5r=3
or r=`3/5`