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 =