Question

The sum of even numbers between $1$ and $31$ is:

• A. $6$
• B. $28$
• C. $240$
• D. $512$

Answer 1

The correct option is C $240$

Let $S_n=(2+4+6+.....+30)$. This is an A.P in which $a=2,d=2$ and $l=30$
Let the number of terms be $n$. Then,
$a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n=15$
$\therefore$ $S_n=\frac{n}{2}(a+l)=\frac{15}{2}\times (2+30)=(15\times 16)=240$.