Question

If \( a_n \) is the \( n \)-th term of A.P. \( 3, 8, 13, 18, \dots \), then what is the value of \( a_{25} - a_{10} \)?

• A. 50
• B. 75
• C. 40
• D. 55

Hint:

The difference between the \( n \)-th and \( m \)-th terms of an A.P. is given by \( (n - m) \times d \). In this case, \( 25 - 10 = 15 \) and \( 15 \times 5 = 75 \).

Answer 1

The Correct Option is B

Step 1: The first term \( a_1 = 3 \) and the common difference \( d = 8 - 3 = 5 \). Step 2: The formula for the \( n \)-th term of an A.P. is: \[ a_n = a_1 + (n - 1) d \] Step 3: Calculate \( a_{25} \) and \( a_{10} \): \[ a_{25} = 3 + (25 - 1) \times 5 = 3 + 120 = 123 \] \[ a_{10} = 3 + (10 - 1) \times 5 = 3 + 45 = 48 \] Step 4: Determine \( a_{25} - a_{10} \): \[ a_{25} - a_{10} = 123 - 48 = 75 \] Thus, the correct answer is \( 75 \), which corresponds to option (B).