*n*(

*n*≠0), there are a finite number of sequences of consecutive integers whose terms add up to

*n*(If

*n*=25, then 3+4+5+6+7=25 is one such sequence with 5 terms).

a. Find an equation for the number of terms of the longest such sequence for any positive integer

*n*.

b. Find equations for the bounds (the first and last terms) of the longest such sequence for any positive integer

*n*.

**Hint:**Once you have an equation for the number of terms, and for the first term of the sequence, the last term is simply one less than their sum.

**Hint 2:** Ducks have absolutely nothing to do with the problem.