For what values of p are 2p + 1, 13, 5p – 3 are three consecutive te

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

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

Answer»

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