Question

The sum of the numbers 12, 24, 36, 48, ......, 120 is

• A. 660
• B. 720
• C. 680
• D. 740

Hint:

Remember: For an arithmetic progression, use \( S_n = \frac{n}{2}(a + l) \) to find the sum quickly.

Answer 1

The Correct Option is A

Step 1: Identify the sequence
The numbers form an arithmetic progression (A.P.) with first term \( a = 12 \), common difference \( d = 12 \).
Step 2: Find the number of terms (\( n \))
Last term \( l = 120 \). The nth term formula is: \[ l = a + (n-1)d. \] Substitute values: \[ 120 = 12 + (n-1) \times 12 \implies 120 - 12 = 12(n-1) \implies 108 = 12(n-1) \implies n - 1 = 9 \implies n = 10. \]
Step 3: Use sum formula for arithmetic progression
Sum of \( n \) terms is: \[ S_n = \frac{n}{2} (a + l) = \frac{10}{2} (12 + 120) = 5 \times 132 = 660. \]
Step 4: Conclusion
The sum of the given numbers is 660.