The value of x for which $(5 x + 2), (4 x - 1)$ and $(x + 2)$ are in A.P. is

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Solution

The correct option is A 3
$∴$ a, b, c are in A.P. if
$2 b = a + c$
$∴ (5 x + 2), (4 x - 1), (x + 2)$ are in A.P.
$2 (4 x - 1) = 5 x + 2 + x + 2$
$\Rightarrow 8 x - 2 = 6 x + 4$
$\Rightarrow 8 x - 6 x = 4 + 2$
$\Rightarrow 2 x = 6 \Rightarrow x = \frac{6}{2}$
$x = 3$

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