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

1. 0

2. 1

3. 2

4. 4

Given,

2p + 1, 13, 5p − 3

In an A.P., the middle term is the average of the first and third terms.

$\Rightarrow 13 = \dfrac{(2p + 1) + (5p - 3)}{2} \\[1em] \Rightarrow 13 = \dfrac{7p - 2}{2} \\[1em] \Rightarrow 13 \times 2 = 7p - 2 \\[1em] \Rightarrow 26 = 7p - 2 \\[1em] \Rightarrow 26 + 2 = 7p \\[1em] \Rightarrow 28 = 7p \\[1em] \Rightarrow 7p = 28 \\[1em] \Rightarrow p = \dfrac{28}{7} \\[1em] \Rightarrow p = 4.$

Hence, option 4 is the correct option.