If $G_{1}, G_{2}, G_{3} . . . . G_{n}$ are n numbers inserted between numbers $a$ and $b$ of a G.P. then common ratio is

(\frac{a}{b})^{\frac{1}{n + 1}}

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(\frac{b}{a})^{\frac{1}{n + 1}}

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(\frac{b}{a})^{n + 1}

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(\frac{a}{b})^{n + 1}

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Solution

The correct option is B $(\frac{b}{a})^{\frac{1}{n + 1}}$
let $a, G_{1}, G_{2}, . . . G_{n}, b$ be in GP

$G_{1} = a r, G_{2} = a r^{2} . . . . G_{n} = a r^{n}$
and $a . b = (a^{2}) . (r^{(n + 1)})$
therefore $r = (\frac{b}{a})^{\frac{1}{n + 1}}$

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