We have already seen an example of iteration when we found the closed formula for arithmetic and geometric sequences. The idea is, we iterate the process of finding the next term, starting with the known initial condition, up until we have \(a_n\text{.}\) Then we simplify. In the arithmetic sequence example, we simplified by multiplying \(d\) by the number of times we add it to \(a\) when we get to \(a_n\text{,}\) to get from \(a_n = a + d + d + d + \cdots + d\) to \(a_n = a + dn\text{.}\)
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