Question

Find the sum of first 20 even terms of the arithmetic sequence.

• A. $420$
• B. $401$
• C. $402$
• D. $403$

Answer 1

The correct option is A $420$

The even series will be $2,4,6,8,\mathrm{10......40}$

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,

$n=$ number of terms $\Rightarrow$ 20
$a=$ first even term $\Rightarrow$ 2
$d=$ common difference of A.P. $\Rightarrow$ 2

substitute the given data in the formula,

$\Rightarrow S_{20}=\frac{20}{2}[2\times 2+(20-1\left)2\right]$

$=10[4+38]$

$=10\left[42\right]$

$=420$

$\therefore$ the sum of first $20$ even terms of the A.P. is $420$.