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Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point) Responses {0,4,16,34} left brace 0 comma 4 comma 16 comma 34 right brace {1,7,12,19} left brace 1 comma 7 comma 12 comma 19 right brace {2,6,11,14} left brace 2 comma 6 comma 11 comma 14 right brace {−6,−1,14,39}

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To determine which polynomial sequence shows constant second differences, we can calculate the first and second differences of each sequence.

  1. For the sequence {0, 4, 16, 34}:

    • First differences: 4-0 = 4, 16-4 = 12, 34-16 = 18 → {4, 12, 18}
    • Second differences: 12-4 = 8, 18-12 = 6 → {8, 6} (not constant)

  2. For the sequence {1, 7, 12, 19}:

    • First differences: 7-1 = 6, 12-7 = 5, 19-12 = 7 → {6, 5, 7}
    • Second differences: 5-6 = -1, 7-5 = 2 → {-1, 2} (not constant)

  3. For the sequence {2, 6, 11, 14}:

    • First differences: 6-2 = 4, 11-6 = 5, 14-11 = 3 → {4, 5, 3}
    • Second differences: 5-4 = 1, 3-5 = -2 → {1, -2} (not constant)

  4. For the sequence {−6, −1, 14, 39}:

    • First differences: -1 - (-6) = 5, 14 - (-1) = 15, 39 - 14 = 25 → {5, 15, 25}
    • Second differences: 15 - 5 = 10, 25 - 15 = 10 → {10, 10} (constant)

The only sequence where the second differences are constant is {−6, −1, 14, 39}.