Question

The sum of the first $16$ terms of the AP: $10,6,2,...$ is

• A. $-320$
• B. $320$
• C. $-400$
• D. $400$

Answer 1

The correct option is A $-320$

Given, $10,6,\mathrm{2.........}$
Since, first term $=10$ and common difference $=6-10=-4$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$S_{16}=\frac{16}{2}\left[2\right(10)+(16-1\left)\right(-4\left)\right]$

$S_{16}=8[20+(15\left)\right(-4\left)\right]$

$S_{16}=8[20-60]$

$S_{16}=8\times (-40)=-320$
Option A is correct.