Question

for what value of p are 2p+1, 13and 5p-3 three consecutive terms of an ap

Answer 1

for terms to be in ap... difference between the two terms should b same
13-(2p+1)=(5p-3)-13
13-2p-1-5p+3+13=0
28-7p=0
p=4

Answer 2

Heya !!!

Given :-

Let 2p+1, 13 and 5p-1 three terms of AP.

We know that in an AP .......
Common difference is same everywhere.
So,

a2-a1 = a3-a2
13 - (2p+1) = 5p-3-13
13 -2p -1 = 5p - 16
12 - 2p = 5p - 16
5p + 2p = 12 + 16
7p = 28
p = 4.

Hence, the value of p should be 4.

Hope you got the answer.

If any doubts, feel free to ask...