Question

The 2nd term of an A.P. is 13 and its 5th term is 25. The common difference of the A.P. is

• A. 5
• B. 4
• C. 3
• D. 6

Hint:

Use the difference of terms to find the common difference when you have two terms of the A.P.

Answer 1

The Correct Option is C

Step 1: The formula for the \( n \)-th term of an A.P. is: \[ a_n = a_1 + (n - 1) d \] Step 2: From the given, - The 2nd term is 13: \[ a_2 = a_1 + (2 - 1) d = a_1 + d = 13 \] - The 5th term is 25: \[ a_5 = a_1 + (5 - 1) d = a_1 + 4d = 25 \] Step 3: Subtract the first equation from the second: \[ (a_1 + 4d) - (a_1 + d) = 25 - 13 \] \[ 3d = 12 \quad \Rightarrow \quad d = 4 \] Thus, the correct answer is \( d = 4 \).