The ratio of the sum of first three terms is to that of first six terms of a GP is 125 : 152. Find the common ratio.

The first three terms of a G.P. are:a,ar,ar2


The first six terms of a G.P. are:a,ar,ar2,ar3,ar4,ar5


It is given that the ratio of the sum of first three terms is to that of first six terms of a GP is 125 : 152.


a + ar + ar2 = 125x & a + ar + ar2 + ar3 + ar4 + ar5 = 152x


a + ar + ar2 + r3( a + ar + ar2) = 152x


125x + r3(125x) = 152x


r3(125x) = 152x - 125x = 27x



r = 3/5


Ans:common ratio =


1