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

n a+a r+a r^2+a r^3+ ... +a r^63 n =7(a+a r^2+a r^4 ... ... +a r^62) n => fraca(1-r^54)1-r=frac7(1-r^54)1-r^2 n r=6n\

If in a G.P. of 64 terms, the sum of all the terms is 7... | Sequence & Series (Mathematics)

\begin{aligned}\n& a+a r+a r^2+a r^3+\ldots+a r^{63} \\\n& =7\left(a+a r^2+a r^4 \ldots \ldots+a r^{62}\right) \\\n& \Rightarrow \frac{a\left(1-r^{54}\right)}{1-r}=\frac{7\left(1-r^{54}\right)}{1-r^2} \\\n& r=6\n\end{aligned}

Explanation

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