Answer
$-1925$.
Work Step by Step
We can see that there are $100$ terms and these terms are part of an arithmetic sequence, so we have:
$a_1=(6)-(1/2)(1)=\dfrac{11}{2} \\ a_{100}=6-(\dfrac{1}{2})(100)=-44$
There is a constant difference between the terms of:
$d=a_{n+1}-a_n=6-\dfrac{1}{2}(n+1) -(6-\dfrac{n}{2})=\dfrac{-1}{2}$
The sum of the first $n$ terms of an arithmetic sequence is given by:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right) ..(1)$
Now, we plug in the above data into Equation-1 to obtain:
$S_{100}= \dfrac{100}{2}[\dfrac{11}{2}+(-44)] \\=(-25)(77) \\= -1925$
Therefore, the sum of the arithmetic sequence is: $-1925$.
