Question

What is the sum of the first nineteenth terms of the arithmetic sequence 2, 6, 10, 14.....?

• A. $522$
• B. $622$
• C. $722$
• D. $822$

Answer 1

The correct option is C $722$

The sum of n terms of an arithmetic sequence can be calculated by $S_n=\frac{n}{2}[2a+(n-1\left)d\right]$
Where, n denotes the total number of terms
$a$= first term
$d=$common difference
$S_n$ = Sum of n terms

$\therefore a=2d=4n=19$
$S=\frac{n}{2}[2\times a+(n-1\left)d\right]$
$S=\frac{19}{2}[2\times 2+(19-1\left)4\right]$
$S=\frac{19}{2}[4+72]$
$S=9.5\left[76\right]$
$S=722$