If the first term of a G.P. $a_{1}, a_{2}, a_{3}, . . . . .$ is unity such that $4 a_{2} + 5 a_{3}$ is least, then the common ratio of G.P. is

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Solution

The correct option is A
$a_{1} = 1, a_{2} = r, a_{3} = r^{2}, . . . .$
$∴ 4 a_{2} + 5 a_{3} = 4 r + 5 r^{2}$
$\frac{d}{d r} (4 r + 5 r^{2}) = 0 \Rightarrow r = \frac{- 2}{5} .$

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