For what value of $k : 2 k, k + 10$ and $3 k + 2$ are in $A P$ ?

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Solution

Since, $2 k, k + 10, 3 k + 2$ are in $A . P$

So,
$\Rightarrow 3 k + 2 - (k + 10) = (k + 10) - 2 k$
$\Rightarrow 3 k - k + 2 - 10 = k - 2 k + 10$
$\Rightarrow 2 k - 8 = - k + 10$
$\Rightarrow 3 k = 18$
$\Rightarrow k = 6$

Hence, this is the answer.

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