Question

Find the sum to $n$ terms of the AP:
5, 2, -1, -4, -7, ...

• A. $\frac{n}{2}(13-3n)$
• B. $n(2-3n)$
• C. $\frac{n}{2}(7+3n)$
• D. $n(n-2)$

Answer 1

The correct option is A

$\frac{n}{2}(13-3n)$

The given sequence is 5, 2, -1, -4, -7, ...., an AP with first term $a=5$ and common difference $d=2-5=-3.$

The sum to $n$ terms of an AP of first term $a$ and common difference $d$ is
$S_n=\frac{n}{2}[2a+(n-1\left)d\right].\Rightarrow S_n=\frac{n}{2}[10+(n-1\left)\right(-3\left)\right]$
$=\frac{n}{2}[10-3n+3]$
$=\frac{n}{2}[13-3n]$