Answer
$10,036$.
Work Step by Step
The nth term of the arithmetic sequence is given by:
$a_n=a_1+(n-1) d \\ 100=4+0.5(n-1) \\192 =(n-1) \\ n= 193$
We see that there is a constant difference between the terms of $d=0.5$ and the terms are part of an arithmetic sequence.
The terms of the sum are the first $193$ terms of an arithmetic sequence, starting with $a_{1}=4$ and with a difference of $d=0.5$.
The sum of the first $n$ terms of an arithmetic sequence is given by:
$S_{n}= \dfrac{n}{2}\left(a_{1}+a_{n}\right)$
Now, $S_{193}= \dfrac{193}{2}[4+100] \\=(193)(52) \\=10, 036$
Therefore, the sum of the arithmetic sequence is: $10,036$.
