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  1. The recursive definition is \(a_n = a_{n-1} + 2\) with \(a_1 = 1\text{.}\) A closed formula is \(a_n = 2n-1\text{.}\)

  2. The sequence of partial sums is \(1, 4, 9, 16, 25, 36, \ldots\text{.}\) A recursive definition is (as always) \(b_n = b_{n-1} + a_n\) which in this case is \(b_n = b_{n-1} + 2n-1\text{.}\) It appears that the closed formula is \(b_n = n^2\)

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