If $(a_1,a_2,\ldots,a_{17})$ satisfy \begin{align*} a_1 + a_2 + a_3 &= 1, \\ a_2 + a_3 + a_4 &= 2, \\ a_3 + a_4 + a_5 &=

If $(a_1,a_2,\ldots,a_{17})$ satisfy \begin{align*} a_1 + a_2 + a_3 &= 1, \\ a_2 + a_3 + a_4 &= 2, \\ a_3 + a_4 + a_5 &= 3, \\ &~~\vdots \\ a_{15} + a_{16} + a_{17} &= 15, \\ a_{16} + a_{17} + a_{1} &= 16, \\ a_{17} + a_{1} + a_{2} &= 17, \end{align*} what is the value of $a_{17}$?