Question

The sum 15+ 30+ 45+.....+ 900 is equal to

• A. 27460
• B. 37450
• C. 27450
• D. 27950

Hint:

Factor out \(15\) from the entire series:
\(15 \times (1 + 2 + 3 + \dots + 60)\).
Use the sum of first \(n\) natural numbers formula, \(\frac{n(n+1)}{2}\):
\(15 \times \frac{60 \times 61}{2} = 15 \times 30 \times 61 = 450 \times 61 = 27450\).

Answer 1

The Correct Option is C

Step 1: Identify the AP parameters.
The series 15, 30, 45, ..., 900 is an AP with first term a = 15 and common difference d = 15.
Step 2: Find the number of terms.
Using l = a + (n - 1)d: 900 = 15 + (n - 1) x 15, so (n - 1) = 59 and n = 60.
Step 3: Apply the sum formula.
Sum = (n/2)(a + l) = (60/2)(15 + 900) = 30 x 915 = 27,450.
\[ \boxed{27450} \]