Question

For what values of p are 2p + 1, 13, 5p – 3 are three consecutive terms of an A.P.?

Answer 1

Given: 2p + 1, 13, 5p – 3 are three consecutive terms of an A.P. 

To find: The value of p 

Solution: Consider a₁ = 2p + 1 , a₂ = 13 and a₃ = 5p – 3

The A.P will be of the form 2p + 1, 13, 5p – 3,.........

Since the terms are in A.P so the common differences in them is same.

⇒ a₂ - a₁ = a₃ - a₂ 

⇒ 13– (2p + 1) = 5p –3 –13

⇒ 13– 2p - 1 = 5p –3 –13 

⇒12– 2p = 5p –16 

⇒12+16 = 5p +2p 

⇒ 28 = 7p

⇒ p= 4