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

Sum of a G.P. series is represented by the formula, , when r≠1. ‘Sn’ represents the sum of the G.P. series upto nth terms, ‘a’ represents the first term, ‘r’ represents the common ratio and ‘n’ represents the number of terms.


Sum of first 3 terms =


Sum of first 6 terms =




152r3 – 152= 125r6-125


125r6-152r3-125+152 = 0


125r6 – 152r3 + 27 = 0


125r6 – 125r3 – 27r3 + 27 = 0


(125r3 - 27) (r3-1)= 0


Either 125r3 -27 = 0 or r3-1 = 0


Either 125r3=27 or r3=1


Either r3 = or r=1


Either r= or r=1


Since r ≠ 1 [ if r is 1, all the terms will be equal which destroys the purpose ]


r =


1