Question

The sum of the first 50 terms of the A.P. \( 2, 4, 6, 8, \dots \) is:

• A. \( 2500 \)
• B. \( 2550 \)
• C. \( 2005 \)
• D. \( 2000 \)

Hint:

The sum of an A.P. can be calculated using \( S_n = \frac{n}{2} [2a + (n-1)d] \).

Answer 1

The Correct Option is B

Step 1: Identify given values In an arithmetic progression (A.P.), the sum of the first \( n \) terms is given by: \[ S_n = \frac{n}{2} [2a + (n-1)d] \] where: - First term \( a = 2 \) - Common difference \( d = 4 - 2 = 2 \) - Number of terms \( n = 50 \) Step 2: Compute the sum \[ S_{50} = \frac{50}{2} [2(2) + (50-1) \times 2] \] \[ = 25 [4 + 49 \times 2] \] \[ = 25 [4 + 98] \] \[ = 25 \times 102 \] \[ = 2550 \] Thus, the correct answer is \( 2550 \).