Question

Find each sum

$2+4+6+....+70$

Short answer

The solution is$S_{35}=1260$

Step-by-step solution

Given information

$2+4+6+....+70$

Calculation

We have, $2+4+6+....+70$

So, $a_1=2,d=2,a_n=70$

Now Use formula,

$$\begin{gathered} a_n=a_1+(n-1)d \\ \Rightarrow 70=2+(n-1)2 \\ \Rightarrow 70=2+2n-2 \\ \Rightarrow 2n=70 \\ \Rightarrow n=35 \end{gathered}$$

Use formula to find sum $S_{35}$

$$\begin{gathered} S_{35}=\frac{35}{2}(2+70) \\ =1260 \end{gathered}$$