Question

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

Answer 1

Let $2p+1,13,5p-3$ be three consecutive term of an AP

Then,

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

$\Rightarrow 13-2p-1=5p-3-13$

$\Rightarrow 12-2p=5p-16$

$\Rightarrow 12+16$=$5p+2p$

$\Rightarrow 28$=$7p$

$\Rightarrow p=4$

Therefore, the value of $p$ is $4$.