To find the second differences of a polynomial sequence, substitute n values into the expression, calculate the terms, and then determine the differences between consecutive terms to identify the second differences.
To find the second differences of the sequence from the polynomial 2n² + 5, we first need to determine the sequence itself by substituting n values into the polynomial expression.
For n = 0, the term is 5; for n = 1, the term is 7; for n = 2, the term is 13; for n = 3, the term is 23, and so on.
Calculating the second differences for this sequence, we get: 2, 2, 2, 2, which shows that the second differences are constant, indicating a quadratic relationship in the original polynomial.
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