Question

The sum of first 16 terms of the A.P.: 10, 6, 2, ..., is
(a) –320
(b) 320
(c) –352
(d) –400

Answer 1

The given A.P. is:
10, 6, 2, ...,

First term = a = 10
Common difference = d = 6 − 10 = −4

$$\begin{gathered} S_{16}=\frac{16}{2}\left[2a+\left(16-1\right)d\right] \\ =8\left[2a+15d\right] \\ =8\left[2\left(10\right)+15\left(-4\right)\right] \\ =8\left[20-60\right] \\ =8\times \left(-40\right) \\ =-320 \end{gathered}$$

​Hence, the correct option is (a).