Question

For what value of p are $(2p+1),13,(5p-3)$ three consecutive terms of an AP?

Answer 1

Let (2p+1), 13,(5p-3) be three consecutive terms of an AP.
Then 13 - (2p+1) =(5p - 3) - 13
⇒ 7p = 28
⇒ p = 4​
∴ When p = 4, (2p+1), 13 and(5p-3) form three consecutive terms of an AP.