If $S = \sum_{n=1}^{15} (n + \frac{1}{3})$ then the value of S is-

Explanation

$S = \sum_{n=1}^{15} (n + \frac{1}{3})$ $= (1+\frac{1}{3}) + (2+\frac{1}{3}) ................. + (15+\frac{1}{3})$ $= \frac{4}{3} + \frac{7}{3} + ........... + \frac{46}{3}$ $= \frac{4+7+............+46}{3}$ $\because S_n = \frac{n}{2}[2a+(n-1)d]$ {where a = 4, d = 3} $= \frac{15}{2}[\frac{2 \times 4 + (15-1)3}{3}] = \frac{\frac{15}{2} \times 50}{3} = \frac{15 \times 25}{3}$ $= 5 \times 25 = 125$