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

Option C is true

Step-by-step explanation:

Given statements:

A. The first difference is constant.

B. The second difference is constant.

C. The third difference is greater than zero.

D. The difference between terms is always positive.

A quadratic sequence is a sequence of numbers in which the second difference between any two consecutive terms is constant.

For example consider a sequence:

0,2,5,9,14,20

Here,

2-0=2

5-2=3

9-5=4

14-9=5

20-14=6

Now, consider sequence: 2,3,4,5,6 (consider terms which are underlined)

Here,

3-2=1

4-3=1

5-4=1

6-5=1

we get a constant sequence in the second time.

B. The second difference is constant.

Step-by-step explanation:

The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant,