AHSME 1993 Problem 21

Let $a_1,a_2,\cdots,a_k$ be a finite arithmetic sequence with $a_4 +a_7+a_{10} = 17$ and $a_4+a_5+\cdots+a_{13} +a_{14} = 77$. If $a_k = 13$, then $k =$ $\text{(A) } 16 \text{(B) } 18 \text{(C) } 20 \text{(D) } 22 \text{(E) } 24$