How this calculator works
A linear number sequence adds the same difference each time. Its first and last values have an average equal to the average of all terms, so multiplying that average by the term count gives the sum. Reverse modes rearrange the endpoint or sum equation. The count includes the initial term: n terms contain n - 1 increments.
Formula
Last L = a + (n-1)d. Sum S = n(a+L)/2. From endpoints, n = (L-a)/d + 1 when d ≠ 0. From a sum, a = S/n - (n-1)d/2.
Worked example
Starting at 2, adding 3 each step and taking 4 terms gives 2, 5, 8, 11. The sum is 4 × (2+11)/2 = 26. From endpoints 5 and 17 over 5 terms, the difference is 3 and the sum is 55.
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Frequently asked questions
Are periods and terms the same?
This page uses the number of terms, including the first value. If you mean a number of increments, add one to get the term count.
Can I sum a decreasing sequence?
Yes. Enter a negative difference. The count still has to be a positive whole number.
Why can a zero step not recover the count?
All endpoints would equal the first value regardless of how many terms there are. The endpoints alone do not determine a unique count.