Choosing a useful form for Sum of Consecutive Integers
Increasing the starting integer by one raises the sum by the number of terms. That behavior gives the sum of consecutive integers output a built-in reasonableness test.
This is an arithmetic-series total; a consecutive product multiplies the run instead. Writing “Consecutive sum” beside the output prevents that mix-up.
Link First integer to its Sum of Consecutive Integers role. Link Number of terms to its Sum of Consecutive Integers role. The retained Sum of Consecutive Integers formula identifies the Sum of Consecutive Integers model.
Consecutive integers differ by one. Their sum is the number of terms multiplied by the average of the first and last terms. To extend Sum of Consecutive Integers, open endpoint averages.
Find the last term as first + count − 1, add the two endpoints, multiply by the count, and divide by two. This result can be carried into arithmetic sequences.
An independent Sum of Consecutive Integers pass needs First integer plus Number of terms. Judge whether Consecutive sum has a plausible sign and scale. Test Number of terms separately; otherwise the cause of a changed Sum of Consecutive Integers Consecutive sum remains unclear.