1992 AJHSME Problems/Problem 15

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Problem

What is the $1992^\text{nd}$ letter in this sequence?

\[\text{ABCDEDCBAABCDEDCBAABCDEDCBAABCDEDC}\cdots\]

$\text{(A)}\ \text{A} \qquad \text{(B)}\ \text{B} \qquad \text{(C)}\ \text{C} \qquad \text{(D)}\ \text{D} \qquad \text{(E)}\ \text{E}$