Question

of S6 of GP is 9 terms S3 of G.P find common ratio​

Answer 1

Answer:

Let the first term be a and common ratio be r.

Given, S6 = 9 × S3

i.e.,

\frac{a( {r}^{6} - 1) }{r - 1} = 9 \times \frac{a( {r}^{3} - 1) }{r - 1} \\ ( {r}^{3} + 1)( {r}^{3} - 1) = 9 \times ( {r}^{3} - 1) \\ {r}^{3} + 1 = 9 \\ {r}^{3} = 8 \\ common \: \: ratio \: \: \: r = 2