2008 Fermat Problem 18

An *arithmetic sequence* is a sequence in which each term after the first is obtained by adding a constant to the previous term.

If the first four terms of an arithmetic sequence are a, 2a, b, and a - 6 - b for some numbers a and b, then the value of the 100th term is

\textbf{(A)}\ -100\quad \textbf{(B)}\ -300\quad \textbf{(C)}\ 150\quad \textbf{(D)}\ -150\quad \textbf{(E)}\ 100

If there are no answer choices shown, enter a numerical answer.

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