Question

A Gp has positive terms. The sum of the first 6 terms Is 9 times the sum of the first three terms. The seventh term is 320

Answer 1

Answer:

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

Given, S6 = 9 × S3

i.e.,

\begin{lgathered}\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\end{lgathered}

r−1

a(r

6

−1)

=9×

r−1

a(r

3

−1)

(r

3

+1)(r

3

−1)=9×(r

3

−1)

r

3

+1=9

r

3

=8

commonratior=2