JEE Mains · Maths · STD 11 - 8. sequence and series
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
- A \(7\)
- B \(4\)
- C \(5\)
- D \(6\)
Answer & Solution
Correct Answer
(D) \(6\)
Step-by-step Solution
Detailed explanation
\( a+a r+a r^2+a r^3+\ldots+a r^{63} \) \(=7\left(a+a r^2+a r^4 \ldots+a r^{62}\right) \) \(\Rightarrow \frac{a\left(1-r^{64}\right)}{1-r}=\frac{7 a\left(1-r^{64}\right)}{1-r^2}\) \(r=6\)
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