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Question:

If $(2 p-1), 7$ and $3 p$ are in $\mathrm{AP}$, find the value of $p$.

Solution:

Let $(2 p-1), 7$ and $3 p$ be three consecutive terms of an AP.

Then $7-(2 p-1)=3 p-7$

$\Rightarrow 5 p=15$

$\Rightarrow p=3$

$\therefore$ When $p=3,(2 p-1), 7$ and $3 p$ form three consecutive terms of an AP.

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