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

Which level differences of this polynomial is a constant value? (1 point)
2nd differences
3rd differences
4th differences
1st differences

1 answer

The formula you provided for the sum of the first n consecutive numbers is actually given by:

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

This is a quadratic polynomial in \( n \).

To find which level differences of this polynomial are constant, we consider the differences:

  1. First differences: Calculate \( S(n+1) - S(n) \).
  2. Second differences: Calculate the first differences of the first differences.
  3. Third differences: Calculate the first differences of the second differences.
  4. Fourth differences: Continue this process.

Since \( S(n) = \frac{n(n+1)}{2} \) is a quadratic polynomial, the first differences will not be constant, but the second differences will be constant.

Thus, the answer is:

2nd differences.