Solve the following equation where each differently numbered a is considered a different variable:
\(\begin{align*} a_1 + a_2 + a_3 &= 1, \\ a_2 + a_3 + a_4 &= 2, \\ a_3 + a_4 + a_5 &= 3, \\ a_4 + a_5 + a_6 &= 4, \\ a_5 + a_6 + a_7 &= 5, \\ a_6 + a_7 + a_8 &= 6, \\ a_7 + a_8 + a_9 &= 7, \\ a_8 + a_9 + a_{10} &= 8, \\ a_9 + a_{10} + a_{11} &= 9, \\ a_{10} + a_{11} + a_{12} &= 10, \\ a_{11} + a_{12} + a_{13} &= 11, \\ a_{12} + a_{13} + a_{14} &= 12, \\ a_{13} + a_{14} + a_{15} &= 13, \\ a_{14} + a_{15} + a_{16} &= 14, \\ a_{15} + a_{16} + a_{17} &= 15, \\ a_{16} + a_{17} + a_{1} &= 16, \\ a_{17} + a_{1} + a_{2} &= 17, \end{align*}\)
