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  • A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

11. A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

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best_answer

Let GP be A_1,A_2,A_3,...................A_2_n

Number of terms = 2n

According to the given condition,

(A_1,A_2,A_3,...................A_2_n)=5(A_1,A_3,...................A_2_n_-_1)

\Rightarrow (A_1,A_2,A_3,...................A_2_n)-5(A_1,A_3,...................A_2_n_-_1)=0

\Rightarrow (A_2,A_4,A_6,...................A_2_n)=4(A_1,A_3,...................A_2_n_-_1)

Let the be GP as a,ar,ar^2,..................

    \Rightarrow \frac{ar(r^n-1)}{r-1}=\frac{4.a(r^{n}-1)}{r-1}

\Rightarrow ar=4a

\Rightarrow r=4

Thus, the common ratio is 4.

Posted by

seema garhwal

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