A geometric series consists of even number of terms. The sum of all terms is $3$ times the sum of odd terms. Find the common ratio.

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Solution

Let the first term of G.P. be $a$ and the common ratio be $r$ .

Let there be $n$ terms.
The sum of all terms $= a (\frac{r^{n} - 1}{r - 1})$

Sum of odd terms $= a (\frac{r^{n} - 1}{r^{2} - 1})$

Given, $a (\frac{r^{n} - 1}{r - 1}) = 3 a (\frac{r^{n} - 1}{r^{2} - 1})$

$\Rightarrow r - 1 = 3 \Rightarrow r = 2$

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