Answer
$-\frac{n(5n+1)}{2}$
Work Step by Step
We simplify:
$\displaystyle \sum_{i=1}^{n}(2-5i)$
We know that we can split up the sums ($\sum{(x+y)}=\sum{x}+\sum{y}$):
$=\sum_{i=1}^{n}2-\sum_{i=1}^{n}5i$
We can take out $5$ because it is a constant $(\sum{cx}=c\sum{x})$:
$=2n-5\sum_{i=1}^{n}i$
We know that $\sum_{i=1}^{n}i=\frac{n(n+1)}{2}$, so:
$=2n-\frac{5n(n+1)}{2}$
$=\frac{4n}{2}-\frac{5n^{2}+5n}{2}$
$=-\frac{4n-5n^2-5n}{2}$
$=-\frac{-n-5n^2}{2}$
$=-\frac{n(5n+1)}{2}$