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> The formula $T\_n = n + (n-1)(n-2)(n-3)(n-4)$ will produce an arithmetic sequence for $n < 5$ but not for $n \ge 5$. Explain why.
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I think it is because if n is less than five the term with multiplication will be equal to zero and the common difference will be one. If n is greater than five, the term added will have multiplication and there will not be a common difference.

Is this correct?