At this point we have two (linear) equations and two unknowns, so we can solve the system for \(a\) and \(b\) (using substitution or elimination or even matrices). We find \(a = \frac{3}{2}\) and \(b = \frac{-1}{2}\text{,}\) so \(a_n = \frac{3}{2} n^2 - \frac{1}{2}n + 2\text{.}\)
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