Question

If the first term of an A.P. is –5 and the common difference is 2, then the sum of first 6 terms is
(a) 0
(b) 5
(c) 6
(d) 15

Answer 1

Given:
First term = a = −5
Common difference = d = 2

$$\begin{gathered} S_6=\frac{6}{2}\left[2a+\left(6-1\right)d\right] \\ =3\left[2a+5d\right] \\ =3\left[2\left(-5\right)+5\left(2\right)\right] \\ =3\left[-10+10\right] \\ =3\times 0 \\ =0 \end{gathered}$$

​Hence, the correct option is (a).