Question

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

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

Hint:

For the sum of an arithmetic sequence: \[ S_n = \frac{n}{2} (2a + (n-1)d) \]

Answer 1

The Correct Option is B

The sum of the first \( n \) terms of an arithmetic progression is given by:
\[ S_n = \frac{n}{2} (2a + (n-1)d) \] Here, \( a = 2 \), \( d = 4 - 2 = 2 \), and \( n = 50 \):
\[ S_{50} = \frac{50}{2} (2(2) + (50-1) \cdot 2) \] \[ = 25 (4 + 98) = 25 \times 102 = 2550 \]