Question

Which of the following statements is correct about quadratic number patterns? A. The first difference is constant. B. The third difference is greater than zero. C. The second difference is constant. D. The difference between terms is always positive

Answer 1

The correct answer option c. is that the second difference in quadratic number patterns is constant. This is indicative of a quadratic relationship between the terms of the pattern.

Step-by-step explanation:

The correct statement about quadratic number patterns is C. The second difference is constant. Quadratic patterns are characterized by a second difference that remains unchanged when you calculate the differences between consecutive terms in the pattern.

To determine the type of pattern, we calculate the first differences (differences between consecutive terms), and if they are not consistent, we then calculate the second differences. If the second differences are consistent, this indicates a quadratic pattern. For example, if we have a pattern with terms 2, 5, 10, 17, the first differences are 3 (5-2), 5 (10-5), and 7 (17-10). The second differences, between the first differences, are 2 (5-3) and 2 (7-5), which are constant, thus indicating a quadratic pattern.