Question

For what value of p are $(2p-1),$ 7 and 3p three consecutive terms of an AP?

Answer 1

Let (2p-1),7 and 3p be three consecutive terms of an AP.
Then 7 - (2p - 1) = 3p - 7
⇒ 5p = 15
⇒ p = 3​
∴ When p = 3, (2p -1), 7 and 3p form three consecutive terms of an AP.