Question 21
Let $a_1,$ $a_2,$ $\ldots,$ $a_k$ be a finite arithmetic sequence with
$$
a_4+a_7+a_{10}=17
$$
and
$$
\begin{aligned} &a_4+a_5+a_6+\cdots+a_{12}\\ &\quad{}+a_{13}+a_{14}=77. \end{aligned}
$$ If $a_k=13,$ then $k=$
$$
a_4+a_7+a_{10}=17
$$
and
$$
\begin{aligned} &a_4+a_5+a_6+\cdots+a_{12}\\ &\quad{}+a_{13}+a_{14}=77. \end{aligned}
$$ If $a_k=13,$ then $k=$