$If (2 m + 5), 4, 3 m are in AP,$
$then m =$ .

\frac{3}{5}

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\frac{2}{5}

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Solution

The correct option is A $\frac{3}{5}$
$Given, (2 m + 5), 4, 3 m are in AP,$

So, the difference between the consecutive terms must be constant.

$\Rightarrow 4 - (2 m + 5) = 3 m - 4$
$\Rightarrow - 1 - 2 m = 3 m - 4$
$\Rightarrow - 5 m = - 4 + 1$
$\Rightarrow - 5 m = - 3$
$\Rightarrow m = \frac{3}{5}$

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