How this calculation works
An even number of consecutive integers can have a half-integer average. Subtracting half the spread must still give an integer starting term.
THE FORMULA
First term = total/count − (count−1)/2A worked example
Three consecutive integers summing to 63 are 20, 21, and 22.
Good to know
Some totals and counts have no integer solution.
Reference: OpenStax Prealgebra (opens in a new tab) ↗
Read the result
Recover a run of consecutive integers from its total and length.
The primary result is labeled “First term”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Some totals and counts have no integer solution.
For a related exercise, try the fraction calculator.
A few questions, answered
How can I check the default inputs by hand?
Three consecutive integers summing to 63 are 20, 21, and 22.
Which rule does this calculator apply?
First term = total/count − (count−1)/2