If in a G.P.

Question

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

Accepted Answer

$$\begin{aligned}
& a+a r+a r^2+a r^3+\ldots .+a r^{63} \
& =7\left(a+a r^2+a r^4 \ldots .+a r^{62}\right) \
& \Rightarrow \frac{a\left(1-r^{64}\right)}{1-r}=\frac{7 a\left(1-r^{64}\right)}{1-r^2} \
& r=6
\end{aligned}$$

Solutions · 1