## College Algebra (10th Edition)

$10,036$
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: $S_{n}=\displaystyle \frac{n}{2}\left(a_{1}+a_{n}\right)$ $S_{193}=\displaystyle \frac{193}{2}\left(4+100\right)=193\cdot 52=10,036$