Question

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

Answer 1

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**.