For a given arithmetic series the sum of the first $50$ terms is $200$, and the sum of the next $50$ terms is $2700$. 
The first term in the series is:
$\textbf{(A)}\ -1221 \qquad \textbf{(B)}\ -21.5 \qquad \textbf{(C)}\ -20.5 \qquad \textbf{(D)}\ 3 \qquad \textbf{(E)}\ 3.5$
Let the first term of the [arithmetic sequence](https://artofproblemsolving.com/wiki/index.php/Arithmetic_sequence) be $a$ and the common difference be $d$.
The $50^{\text{th}}$ term of the sequence is $a+49d$, so the sum of the first $50$ terms is $\frac{50(a + a + 49d)}{2}$.
The $51^{\text{th}}$ term of the sequence is $a+50d$ and the $100^{\text{th}}$ term of the sequence is $a+99d$, so the sum of the next $50$ terms is $\frac{50(a+50d+a+99d)}{2}$.
Substituting in values results in this [system of equations](https://artofproblemsolving.com/wiki/index.php/System_of_equations).
\[2a+49d=8\]
\[2a+149d=108\]
Solving for $a$ yields $a = \frac{-41}{2}$.  The first term is $-20.5$, which is answer choice $\boxed{\textbf{(C)}}$.