Question

Find each sum.

$2+4+6+\dots .+2n$

Short answer

The required answer is$S_n=n+n^2$

Step-by-step solution

Given information

$2+4+6+\dots .+2n$

Calculation

We have, $2+4+6+\dots .+2n$

So, $a_1=2,d=2,a_n=2n$

Now use formula,

$$\begin{gathered} S_n=\frac{n}{2}(a_1+a_n) \\ =\frac{n}{2}(2+2n) \\ =\frac{n}{2}\times 2+\frac{n}{2}\times 2n \\ =n+n^2 \end{gathered}$$

Therefore the sum is$S_n=n+n^2$