Question

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

• A. $16$
• B. $128$
• C. $240$
• D. $512$

Answer 1

The correct option is C $240$

Required sum $=(2+4+6+......+30)$
This is an A.P in which $a=2,d=(4-2)=2$ and $l=30$.
Let the number of terms be $n$. Then,
$t_n=30$ $\Rightarrow$ $a+(n-1)d=30$
$\Rightarrow$ $2+(n-1)\times 2=30$
$\Rightarrow$ $n-1=14$
$\Rightarrow$ $n=15$
$\therefore$ $S_n=\frac{n}{2}(a+l)=\frac{15}{2}\times (2+30)=240$