Question

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

Answer 1

Here, we are given three terms,

First term (a₁) = 2p + 1

Second term (a₂) = 13

Third term (a₃) = 5p - 3 

We need to find the value of p for which these terms are in A.P. So, in an A.P. the difference of two adjacent terms is always constant. So, we get,

d = a₂ - a₁

d = 13 - (2p + 1)

d = 13 - 2p - 1

d = 12 - 2p                           .............(1)

Also,

d = a₃ - a₂

d = (5p - 3) - 13

d = 5p - 3 - 13

d = 5p - 16                      ..................(2) 

Now, on equating (1) and (2), we get,

12 - 2p = 5p - 16

5p + 2p = 16 + 12

7p = 28

`p = 28/7`

p = 4

Therefore, for p = 4, these three terms will form an A.P.