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

Answer

`(8+24/5+72/25+...oo)`

Explanation

Let a abe the first term and r be the common ratio of the given series.
Then, `a/((1-r))=20 rArr a^(2)/((1-r)^(2))=400` ...(i)
And, `a^(2)/((1-r^(2)))=100` ...(ii)
`:. a^(2)/((1-r)^(2))xx((1-r^(2)))/a^(2)=400/100 rArr (1+r)/(1-r)=4 rArr r=3/5`
`:. a/((1-3/5))=20 rArr a=8`.
Hence, the required series is `(8+24/5+72/25+...oo)`.