Answer : Sum of a G.P. series is represented by the formula,  when r≠1. ‘Sn’ represents the sum of the G.P. series upto n^th 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 ]