The sum of a sequence of consecutive numbers from 1 to n is given by the formula n(n+1)2

Question

Which level differences of this polynomial is a constant value?(1 point)
Responses

2nd differences
2nd differences

3rd differences
3rd differences

4th differences
4th differences

1st differences

Answer 1

The sum of the sequence of consecutive numbers from 1 to n is given by the formula:

\[ S(n) = \frac{n(n+1)}{2} \]

This is a quadratic polynomial. When we go through the process of calculating differences of a polynomial, we find that:

1. The 1st differences (which are the differences between consecutive values of the function) are linear.
2. The 2nd differences (which are the differences of the 1st differences) are constant.

Since \(S(n)\) is a quadratic function, the constant value appears in the 2nd differences.

Therefore, the correct response is:

2nd differences