Question

If the sum of first n terms of an A.P. is given by \( S_n = \frac{n}{2}(3n+1) \), then the first term of the A.P. is

• A. 2
• B. \( \frac{3}{2} \)
• C. 4
• D. \( \frac{5}{2} \)

Answer 1

The Correct Option is A

The sum of the first \(n\) terms of an A.P. is given by \( S_n = \frac{n}{2}(3n+1) \). The first term of an A.P., \( a_1 \), is equal to the sum of the first 1 term, \( S_1 \). To find the first term, we substitute \( n = 1 \) into the formula for \( S_n \): \[ S_1 = \frac{1}{2}(3(1)+1) \] \[ S_1 = \frac{1}{2}(3+1) \] \[ S_1 = \frac{1}{2}(4) \] \[ S_1 = 2 \] Therefore, the first term of the A.P. is 2. \[ \boxed{2} \]