Answer
$1260$
Work Step by Step
We have to determine the sum:
$S=2+4+6+.....+70$
As $4-2=6-4=...=2$, the sequence is arithmetic.
Determine its first term and the common difference:
$a_1=2$
$d=2$
The given sum contains $\dfrac{70}{2}=35$ terms; therefore we have to determine the sum of the first $35$ terms. We use the formula:
$S_n=\dfrac{n(a_1+a_n)}{2}$
$2+4+6+...+70=\dfrac{35(2+70)}{2}$
$=\dfrac{35\cdot 72}{2}$
$=1260$
