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First, if you look at the differences between terms, you get a sequence of differences: \(1,4,7,10,13, \ldots\text{,}\) which is an arithmetic sequence. Written another way:

\begin{align*} a_0 \amp = 2\\ a_1 \amp = 2+1\\ a_2 \amp = 2+1+4\\ a_3 \amp = 2+1+4+7 \end{align*}

and so on. We can write the general term of \((a_n)\) in terms of the arithmetic sequence as follows:

\begin{equation*} a_n = 2 + 1 + 4 + 7 + 10 + \cdots + (1+3(n-1)) \end{equation*}

(we use \(1+3(n-1)\) instead of \(1+3n\) to get the indices to line up correctly; for \(a_3\) we add up to 7, which is \(1+3(3-1)\)).

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