Question

What are the 2nd differences of the sequence from the following polynomial? n^2 n 1

a) 2, 2
b) 2, 1
c) 1, 1
d) 3, 3

Answer 1

The 2nd differences of a sequence from the polynomial n^2 are constant, and they are 2 for each term. This supports that the sequence is quadratic, aligning with answer choice (a) 2, 2.

Step-by-step explanation:

The question asks about the 2nd differences of a sequence from a given polynomial, which is indicative of a quadratic sequence where the second differences are constant. In a sequence formed from the polynomial function n2, the first terms would be 12 = 1, 22 = 4, 32 = 9, and so on. The first differences, found by subtracting each term from the subsequent term, would be 4-1=3, 9-4=5, 16-9=7, etc. The second differences are then found by subtracting each first difference from the next first difference, which in this case would be 5-3=2, 7-5=2, and so on. Therefore, the second differences are constant at 2, which confirms that the sequence is indeed quadratic and corresponds to answer choice (a) 2, 2.