A G.P. consist of an even number of terms. If the sum of all the terms is 5 times the sum of the ter

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A G.P. consist of an even number of terms. If the sum of all the terms is 5 times the sum of the terms occupying the odd places. Then the common ratio will be equal to

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Sol. [Key Concept: G.P. with even count: sum $= 5 	imes$ (odd-place sum) ⇒ a relation in the common ratio.]Let $a,ar,{ar}^{2},\ldots\ldots{ar}^{2n - 1}$$$\begin{matrix} & & \frac{a\left( 1 - r^{2n} ight)}{1 - r} & = \frac{5a\left( 1 - \left( r^{2} ight)^{n} ight)}{1 - r^{2}} \ \Rightarrow & & & r = 4 \end{matrix}$$

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