Question

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

• A. \( 3 \)
• B. \( 4 \)
• C. \( 12 \)
• D. \( 6 \)

Hint:

In an A.P., if three terms are given, use \( 2b = a + c \) to find missing variables.

Answer 1

The Correct Option is D

For an A.P., the difference between consecutive terms must be equal:
\[ 13 - (2p + 1) = (5p - 3) - 13. \] \[ 12 - 2p = 5p - 16. \] Solving for \( p \):
\[ 12 + 16 = 5p + 2p. \] \[ 28 = 7p. \] \[ p = 6. \]