Question

For what value of p, are 2p+1,13,5p-3 three consecutive terms of an AP?

Answer 1

If the three terms are consecutive terms of an AP,
common difference, d = a2-a1 = a3-a2
Here, a1 = 2p+1, a2 = 13 and a3 = 5p-3

=> d= 13 - (2p+1) = (5p-3) - (13)
=> 12 - 2p = 5p - 16
=> 7p = 28
=> p = 4

Hence, value of p for which the given terms are consecutive terms of an AP is 4