# Solve this

Question:

If $(2 p+1), 13,(5 p-3)$ are in AP, find the value of $p$.

Solution:

Let $(2 p+1), 13,(5 p-3)$ be three consecutive terms of an AP.

Then $13-(2 p+1)=(5 p-3)-13$

$\Rightarrow 7 p=28$

$\Rightarrow p=4$

$\therefore$ When $p=4,(2 p+1), 13$ and $(5 p-3)$ form three consecutive terms of an AP.