Consecutive integers are whole numbers that follow one another with a step of one. Their pattern makes an unknown sequence possible to reconstruct from its sum.
Use this when a word problem says consecutive, consecutive even, or consecutive odd numbers and asks for the missing sequence.
The key rule
What stays true
sum = n(2a + (n−1)d) / 2
See the idea
Visual explanation
15+16+17= 48
Example
Apply it
15 + 16 + 17 = 48
A requested sum may not produce a whole-number first term, so no matching integer sequence exists.
Quick guide
How to use this calculator
Enter the target integer sum.
Choose 2–1,000 terms and spacing 1 or 2.
Read the unique sequence or the truthful no-solution state.
Calculation method
Solve the arithmetic-sequence sum
For first term a, count n, and step d, the sum is n(2a+(n−1)d)/2. Rearranging gives a; an integer sequence exists only when that value is integral.
Worked example
Three integers adding to 48
Subtract the spacing contribution 3, then divide 45 by 3 to get the first term 15.
15 + 16 + 17 = 48
Supported inputs
Precision and limits
Count
Choose from 2 through 1,000 terms.
Spacing
Step 1 gives consecutive integers; step 2 gives consecutive values of the same parity.
