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Note that now we can guess a closed formula for the \(n\)th term of the sequence: \(a_n = n+3\text{.}\) To be sure this will always work, we could plug in this formula into the recurrence relation:

\begin{align*} 2a_{n-1} - a_{n-2} \amp = 2((n-1) + 3) - ((n-2) + 3)\\ \amp = 2n + 4 - n - 1\\ \amp = n + 3\\ \amp = a_n\text{.} \end{align*}

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