The sum of a sequence of consecutive numbers from 1 to n is given by the formula n(n+1)2. Which level differences of this polynomial is a constant value?(1 point)
1st differences
4th differences
2nd differences
3rd differences
2nd differences
The level differences of a polynomial can be found by subtracting consecutive terms in the polynomial. In this case, we need to find the level differences of the polynomial n(n+1)/2.
Let's calculate the level differences for the given polynomial:
1st difference:
(n+1)/2 - n/2 = 1/2
2nd difference:
(1/2) - (n+1)/2 = -n/2
3rd difference:
(-n/2) - (1/2) = -1/2 - n/2 = -(n+1)/2
4th difference:
(-(n+1)/2) - (-n/2) = -n/2 + n/2 = 0
After calculating the first, second, third, and fourth differences, we find that the 4th differences are a constant value of 0. Therefore, the correct answer is:
4th differences.