Question

The sum of 15 terms of A.P. 3, 6, 9,...

• A. 315
• B. 360
• C. 415
• D. 460

Answer 1

The Correct Option is B

To solve the problem, we need to find the sum of the first 15 terms of the arithmetic progression (A.P.) 3, 6, 9, ...

1. Identifying the First Term and Common Difference:
First term \( a = 3 \)
Common difference \( d = 6 - 3 = 3 \)

2. Using the Formula for Sum of First \( n \) Terms:
The sum of the first \( n \) terms of an A.P. is given by:
\[ S_n = \frac{n}{2} [2a + (n - 1)d] \]

3. Substituting the Values:
Let \( n = 15 \), \( a = 3 \), \( d = 3 \)
\[ S_{15} = \frac{15}{2} [2 \times 3 + (15 - 1) \times 3] \\ = \frac{15}{2} [6 + 42] \\ = \frac{15}{2} \times 48 = \frac{720}{2} = 360 \]

Final Answer:
The sum of 15 terms of the A.P. is 360 (Option B).