Question

The terms 4, 7, 10, \dots form an A.P. The sum of the first 15 terms is?

• A. 340
• B. 360
• C. 375
• D. 390

Hint:

To find the sum of terms in an A.P., use the formula \( S_n = \frac{n}{2} (2a + (n-1) d) \).

Answer 1

The Correct Option is C

Step 1: Using the formula for the sum of an A.P.
The sum \( S_n \) of the first \( n \) terms of an A.P. is given by: \[ S_n = \frac{n}{2} \left( 2a + (n - 1) d \right) \] where \( a \) is the first term, \( d \) is the common difference, and \( n \) is the number of terms. Step 2: Substitute the given values.
We are given that:
\( a = 4 \)
\( d = 7 - 4 = 3 \)
\( n = 15 \)
Now substitute these values into the sum formula: \[ S_{15} = \frac{15}{2} \left( 2 \times 4 + (15 - 1) \times 3 \right) \] Simplify the expression: \[ S_{15} = \frac{15}{2} \left( 8 + 42 \right) = \frac{15}{2} \times 50 = 15 \times 25 = 375 \]