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A)Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point)

Responses

{0,4,16,34}

{2,6,11,14}

{−6,−1,14,39}

{1,7,12,19}

1 answer

To determine which polynomial sequence has constant 2nd differences, we need to calculate the first and second differences for each of the given sequences.

  1. {0, 4, 16, 34}
    First differences:
    4 - 0 = 4
    16 - 4 = 12
    34 - 16 = 18
    (First differences: 4, 12, 18)
    Second differences:
    12 - 4 = 8
    18 - 12 = 6
    (Second differences: 8, 6) → Not constant

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

  3. {−6, −1, 14, 39}
    First differences:
    -1 - (-6) = 5
    14 - (-1) = 15
    39 - 14 = 25
    (First differences: 5, 15, 25)
    Second differences:
    15 - 5 = 10
    25 - 15 = 10
    (Second differences: 10, 10) → Constant

  4. {1, 7, 12, 19}
    First differences:
    7 - 1 = 6
    12 - 7 = 5
    19 - 12 = 7
    (First differences: 6, 5, 7)
    Second differences:
    5 - 6 = -1
    7 - 5 = 2
    (Second differences: -1, 2) → Not constant

From the calculations, only the sequence {−6, −1, 14, 39} shows constant second differences.

So, the answer is: {−6, −1, 14, 39}.