Calculating it by hand
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.
Math calculator
Sum of Consecutive Integers Calculator
Add a specified run of consecutive integers beginning from any whole-number starting point. The result panel keeps consecutive sum and its numerical trail together.
Sum of Consecutive Integers inputs
Provide the numbers
Follow one set of numbers
Starting at 12 for eight terms ends at 19. The average endpoint is 15.5, and 8 × 15.5 gives a sum of 124.
Practical meaning
Runs of dates, numbered seats, serial ranges, and arithmetic-series exercises can be totaled without entering every intermediate integer. A related application of Sum of Consecutive Integers is consecutive products.
Mathematical foundation
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.
Reading consecutive sum in Sum of Consecutive Integers requires the relationship defined above.
Where the shortcut stops
The count must be a positive integer. A negative starting value is valid, and a run crossing zero may have a small or zero total.
Record the units for Sum of Consecutive Integers beside each source value; the reader must still confirm compatibility while performing sum of consecutive integers.
What to record with the answer
Before entering first integer and number of terms, identify what each field represents. Its label determines how the sum of consecutive integers relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
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.
A final answer should carry enough context to be reusable: name it consecutive sum, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied inputs in the fields and the displayed formula are more informative than the decimal alone.
This is an arithmetic-series total; a consecutive product multiplies the run instead. Writing “Consecutive sum” beside the output prevents that mix-up.
A useful note for this result contains the supplied inputs (first integer and number of terms), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
Questions about Sum of Consecutive Integers
Can the first integer be negative?
Yes.
Why can the endpoint average be a half-integer?
An even number of consecutive terms can have its center halfway between two integers.
Does order affect the sum?
No, but the specified first term identifies which integers belong to the run.
What if count is one?
The sum equals the first integer.