Question

IF (2p-1), 7, 3p are in AP, find hte value of p.

Answer 1

Given: (2p – 1), 7, 3p are three consecutive terms of an A.P.

As we know that,

Common difference (d) of an A.P. can be obtained by subtracting any two consecutive terms.

⇒ d = 7 – (2p – 1)

⇒ d= 7 – 2p + 1

⇒ d= 8 – 2p ... (1)

Also,

d = 3p – 7 ... (2)

Now,

On equating (1) and (2), we get,

⇒8 – 2p = 3p – 7

⇒ 3p + 2p = 8 + 7

⇒ 5p = 15

⇒ p = = 3

Thus, the value of p is 3 and the three consecutive terms of the A.P. are (2 × 3 – 1), 7, (3 × 3) = 5, 7, 9