If the first term of the G.P is unity, and value of `4a_2+5a_3` is minimum then find the sum to infinite terms

The first term of a GP is unity. For what value of the common ratio of the progression the sum of 4 times the second term and 5 times the third term will be minimum ?

If the first term of an infinite G.P. is 8 and its sum to infinity (32)/5 then find the common ratio.

Suppose that a, ar, ar^2,ar^3,ar^4,ar^5 are the first 6 terms of a G.P Find the ratio of the sum of the first tree terms and the sum of first 6 terms

If the first term of an infinite G.P. is 1 and each term is twice the sum of the succeeding terms, then the sum of the series is

If the first term of an infinite G.P. is 8 and its sum to infinity is (32)/(3) then find the common ratio.

The first term of an infinite G.P. is a and its sum is 3, then-

In a G.P.the product of the first four terms is 4 and the second term is the reciprocal of the fourth term.The sum of infinite terms of the G.P is

The first term of an infinitely decreasing G.P.is unity and its sum is S .The sum of the squares of the terms of the progression is

In a G.P. the product of the first four terms is 4 and the second term is the reciprocal of the fourth term. The sum of infinite terms of the G.P is