Question

Determine the sum of the arithmetic series $10+20+30+...600.$

• A. $13500$
• B. $15500$
• C. $18300$
• D. $19100$

Answer 1

The correct option is C $18300$

$a_n=a+(n-1)d$
$\Rightarrow 600=10+(n-1)10$
$\Rightarrow 600-10=10n-10$
$\Rightarrow 590+10=10n$
$\Rightarrow 600=10n$
$\Rightarrow n=60$

$S_n=\frac{n}{2}[a_1+a_n]$
$\Rightarrow S_n=\frac{60}{2}[10+600]$
$\Rightarrow S_n=30\left[610\right]$
$\Rightarrow S_n=18300$