Identify which of the sets is not the solution set of the following system of equations.
\[ \begin{aligned} \frac12 x-y&=3 \\ \frac x3 - \frac23 y &=2 \end{aligned} \]
We are given a sequence \( \left( a_n \right)^{\infty}_{n=1} \) defined recursively by: \( a_1=1,\ a_2=2\,;\ a_{n+2}=\frac12\left( a_{n+1}+a_n\right),\ n\in\mathbb{N} \).
Find the sum of the first four terms of this sequence.