Sum of infinite number of terms in G.P. is and sum of their square is . The common ratio of G.P. is
Explanation for the correct option :
Step 1 : Using the sum formula of an infinite G.P.
Let be the G.P. series where is initial term and is common difference.
Formula to be used : We know that the the sum of the terms of an infinite G.P. with the initial term and common ratio is .
Given that the sum of the G.P. is . So, we must get
Now, squaring each term of the series, we get the series with the following terms :
This is again an infinite G.P. with initial term and common difference .
Therefore, the sum of infinite terms of this G.P. is .
But sum is given as . Hence, we get
Step 2 : Solving equations and to find the value of
The two equations obtained are :
Squaring both sides of equation , we get :
Divide equation by equation , we obtain :
Therefore, option (B) is the correct option.