Question

Find the sum of first 100 even natural numbers.

• A. \(10100 \)
• B. \(11020 \)
• C. \(10080 \)
• D. \(10050 \)
• E. \(10070 \)

Hint:

Sum of first $n$ even numbers: \[ S = n(n+1) \] This is much faster than adding terms manually.

Answer 1

The Correct Option is A

Concept: The first $n$ even natural numbers form an Arithmetic Progression (A.P.): \[ 2, 4, 6, \ldots, 2n \] Sum of first $n$ even numbers: \[ S_n = n(n+1) \]
Step 1: Use the formula.
\[ S_{100} = 100 \times 101 \]

Step 2: Calculate the value.
\[ S_{100} = 10100 \]