The terms of a sequence are defined by $a_{n} = 3a_{n - 1} - a_{n - 2}$ for $n > 2$. Find the value of $a_{5}$ given that $a_{1} =4$ and $a_{2} = 3$.

Using the given recursive formula, the third term is 3 times 3 minus 4, which equals 5. The fourth term is 3 times 5 minus 3, which equals 12. The fifth term is 3 times 12 minus 5, resulting in 31.

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