If the numbers $4 p + 1, 26, 10 p - 5$ are in $A . P .$ Find the value of $p$ .

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Solution

Difference between consecutive terms in AP is constant.
$\Rightarrow 26 - (4 p + 1) = 10 p - 5 - 26$
$\Rightarrow 26 - 4 p - 1 = 10 p - 31$
$\Rightarrow 14 p = 56$
$\Rightarrow p = 4$ .

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