Consider
$\begin{array}{rcl}
a_3 & = & a_1 + a_2 \\
21 & = & a_1 + a_2 \\
a_1 & = & 21 – a_2 \ \ldots \unicode{x2460}
\end{array}$
Consider
$\begin{array}{rcl}
a_4 & = & a_2 + a_3 \\
a_4 & = & a_2 + 21 \\
a_2 & = & a_4 – 21 \ \ldots \unicode{x2461}
\end{array}$
Sub. $\unicode{x2461}$ into $\unicode{x2460}$, we have
$\begin{array}{rcl}
a_1 & = & 21 – (a_4 – 21) \\
a_1 & = & 42 – a_4 \ \ldots \unicode{x2462}
\end{array}$
Consider
$\begin{array}{rcl}
a_5 & = & a_3 + a_4 \\
a_5 & = & 21 + a_4 \\
a_5 – a_4 & = & 21 \ \ldots \unicode{x2463}
\end{array}$
Consider
$\begin{array}{rcl}
a_6 & = & a_4 + a_5 \\
a_4 + a_5 & = & 89 \ \ldots \unicode{x2464}
\end{array}$
$\unicode{x2464} – \unicode{x2463}$, we have
$\begin{array}{rcl}
2a_4 & = & 68 \\
a_4 & = & 34
\end{array}$
Sub. $a_4 = 34$ into $\unicode{x2462}$, we have
$\begin{array}{rcl}
a_1 & = & 42 – 34 \\
a_1 & = & 8
\end{array}$
