Question

If \(\sum_{n=45}\), then n= ____

• A. 9
• B. 10
• C. 11
• D. 12

Answer 1

The Correct Option is A

To solve this problem, we need to determine the value of \( n \) such that the sum of the first \( n \) natural numbers is 45.

1. Formula for Sum of First \( n \) Natural Numbers:
The formula is:

\( S_n = \frac{n(n + 1)}{2} \)

2. Substituting the Given Sum:
We are given \( S_n = 45 \), so:

\( \frac{n(n + 1)}{2} = 45 \)

3. Multiply Both Sides by 2:
\( n(n + 1) = 90 \)

4. Solving the Equation:
We try values of \( n \) to satisfy the equation:
Try \( n = 9 \): \( 9 \times 10 = 90 \) ✅

Final Answer:
The correct option is (A) 9.