Question

Which polynomial sequence shows that the terms of the 2nd differences are constant? (1 point) Responses {−6,−1,14,39} left brace negative 6 comma negative 1 comma 14 comma 39 right brace {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}

Answer 1

Among the given sequences, the one with constant 2nd differences is the sequence {−6, −1, 14, 39}. The 2nd differences are constant at 10.

Explanation:

To determine which polynomial sequence has constant 2nd differences, we need to calculate the 2nd differences for each sequence and see if they are constant.

Let's calculate the 2nd differences for each sequence:

Sequence {−6, −1, 14, 39}:

1st differences: 5, 15, 25

2nd differences: 10, 10

Sequence {0, 4, 16, 34}:

1st differences: 4, 12, 18

2nd differences: 8, 6

Sequence {1, 7, 12, 19}:

1st differences: 6, 5, 7

2nd differences: -1, 2

Sequence {2, 6, 11, 14}:

1st differences: 4, 5, 3

2nd differences: 1, -2

Among the given sequences, the one with constant 2nd differences is the sequence {−6, −1, 14, 39}. The 2nd differences are constant at 10.

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