Find the maximum value of the first number in a set

Could you help me out with a piece of homework, I really do not know, how to solve this. Even how to begin.

$8$ natural numbers are written in a row. Each number, beginning from the third is a sum of last two numbers before it. Which maximum value has the first number if the last is $2018$?

Hope that my knowledge is solid enough for this task.

Answer

so far we know there are 8 numbers, so we can name them $$a_1,a_2,\ldots,a_8$$, and every number starting from 3rd the sum of two previous ones. so we know $$\begin{eqnarray}
a_3 &=& a_2+a_1 &=& 1*&a_2&+1*&a_1& \\
a_4 &=& a_3+a_2 &=& 2*&a_2&+1*&a_1& \\

a_5 &=& a_4+a_3 &=& 3*&a_2&+2*&a_1& \\
a_6 &=& a_5+a_4 &=& 5*&a_2&+3*&a_1& \\
a_7 &=& a_6+a_5 &=& 8*&a_2&+5*&a_1& \\
a_8 &=& a_7+a_6 &=& 13*&a_2&+8*&a_1& \\
\end{eqnarray}$$

so we know whatever values we choose for $a_1$ and $a_2$, we will always get $a_8=13*a_2+8*a_1$ and from the problem we know $a_8= 2018$. the rest is easy, you just have to minimize value for $a_2$ (eg. $a_2 = 2$) and calculate the value for $a_1$ (which would be 249)