Given:
Sum of G.P of 3 terms is 125
By using the formula,
Sum of GP for n terms = a(rn – 1 )/(r – 1)
125 = a (rn – 1)/(r - 1)
125 = a (r3 – 1)/ (r - 1) … equation (1)
Now,
Sum of G.P of 6 terms is 152
By using the formula,
Sum of GP for n terms = a(rn – 1 )/(r – 1)
152 = a (rn – 1)/(r - 1)
152 = a (r6 – 1)/ (r - 1) … equation (2)
Let us divide equation (i) by (ii) we get,
125/152 = [a (r3 – 1)/ (r - 1)] / [a (r6 – 1)/ (r - 1)]
125/152 = (r3 – 1)/(r6 – 1)
125/152 = (r3 – 1)/[(r3 – 1) (r3 + 1)]
125/152 = 1/(r3 + 1)
125(r3 + 1) = 152
125r3 + 125 = 152
125r3 = 152 – 125
125r3 = 27
r3 = 27/125
r3 = 33/53
r = 3/5
∴ The common ratio is 3/5