Question

For what value of \( p \), the terms \( (2p + 1), 13, (5p - 3) \) are in A.P.?

• A. 3
• B. 4
• C. 12
• D. 6

Hint:

For three numbers to be in A.P., the middle term must be the average of the first and third terms.

Answer 1

The Correct Option is B

Step 1: For the terms to be in A.P., the middle term must be the average of the first and third terms. \[ 13 = \frac{(2p + 1) + (5p - 3)}{2} \] Step 2: Solve for \( p \): \[ 13 = \frac{2p + 1 + 5p - 3}{2} \] \[ 13 = \frac{7p - 2}{2} \] \[ 26 = 7p - 2 \] \[ 28 = 7p \] \[ p = 4 \] Thus, the correct answer is \( p = 4 \).