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Common Difference

Find the valu...

Question

Find the value of $k$ , If $x, 2 x + k, 3 x + 5$ are consecutive terms in A.P.

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Solution

If $x, 2 x + k, 3 x + 5$ are in A.P
$\Rightarrow 2 x + k - x = 3 x + 5 - 2 x - k$
$\Rightarrow x + k = x + 5 - k$
$\Rightarrow k = 5 - k$
$\Rightarrow 2 k = 5$
$∴ k = \frac{5}{2}$

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