Item 3.

This is the Fibonacci sequence. The sequence of first differences is \(0, 1, 1, 2, 3, 5, 8, \ldots\text{,}\) the second differences are \(1, 0, 1, 1, 2, 3, 5\ldots\text{.}\) We notice that after the first few terms, we get the original sequence back. So there will never be constant differences, so the closed formula for the Fibonacci sequence is not a polynomial.

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