Sum of infinite number of terms in GP is 20 and sum of their square is 100

• Sequences Series

Sum of infinite number of terms in GP is 20 and sum of their square is 100. The common ratio of GP is

1. 1/5
2. 3/5
3. 8/5
4. 5

Answer

Let terms of GP be a, ar, ar²

where a = first term, r = common ratio

S_∞ = a/1-r

Therefore, a/1-r = 20

a = 20(1-r)

Also, a² = 100(1 - r²)

The correct option is B.