**Question:**

**If ratio of sum of first 6 terms of G.P. to sum of first 3 terms of G.P. is 9:1, what is the common ratio of G.P.?**

**Solve**

In the question it is given that

S^{6}/ S^{3} = 9/1

Therefore, we have to find the value of â€˜râ€™.

{a(r^{6}-1)/(r-1)} / {a(r^{3}-1)/(r-1)} = 9/1

(r^{6}-1) / (r^{3}-1) = 9/1

(r^{3}+1)(r^{6}-1) / (r^{6}-1) = 9/1

r^{3}+1 = 9

r^{3} = 9-1

r^{3} = 8

r = 2

Check out more examples of Geometric Progression (G.P.), explained lucidly.