Question

select the correct answer.
which of the following statements is correct about quadratic number patterns?
a. the first difference is constant.
b. the difference between terms is always positive.
c. the third difference is greater than zero.
d. the second difference is constant.

Explanation:

To determine the correct statement about quadratic number patterns, we analyze each option:

• Option A: In a linear number pattern, the first difference is constant. For a quadratic pattern, the first difference is not constant (it follows a linear pattern), so A is incorrect.
• Option B: The difference between terms in a quadratic pattern can be negative (e.g., for a downward - opening quadratic sequence), so B is incorrect.
• Option C: Quadratic number patterns have a constant second difference, and there is no third difference (the second difference does not change), so C is incorrect.
• Option D: By the definition of a quadratic number pattern, the second difference (the difference of the first differences) is constant. This is a key characteristic of quadratic sequences.

Answer:

D. The second difference is constant.