Answer
The sum of the first $n$ terms of the arithmetic sequence is: $1260$.
Work Step by Step
The sum of the first $n$ terms of the arithmetic sequence is given by:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right)$
Rearrange the terms as: $2+4+6+..+70 =2+(2+2)+(2+2 \cdot 2)+.+(2+34 \cdot 2)$
We see that there is a constant difference between the terms of $d=4-2=2$ or, $d=6-4=2$
The terms of the sum are the first $35$ terms of the arithmetic sequence, starting with $a_{1}=2$ .
Now, $S_{35}= \dfrac{n}{2}[2+70]\\=(35)(36) \\=1260$
Therefore, the sum of the first $n$ terms of the arithmetic sequence is: $1260$.
