Answer
$10,036$
Work Step by Step
There is a constant difference, $0.5$, between terms.
The terms are part of an arithmetic sequence.
nth Term of an Arithmetic Sequence:
$a_{n}=a_{1}+(n-1)d$
$ 100=4+0.5(n-1)\qquad$... solve for n
$96=0.5(n-1)$
$192=(n-1)$
$n=193$
There are $193$ terms in the sum.
The terms of the sum
are the first $193$ terms of an arithmetic sequence, $a_{1}=4, d=0.5.$
Sum of the First $n$ Terms of an arithmetic sequence:
$S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$
$S_{193}=\displaystyle \frac{193}{2}\left(4+100\right)=193\cdot 52=10,036$
