Arithmetic Series Sum
Calculate the sum of the first n terms of an arithmetic sequence.
How to use
- Enter first term a, number of terms n, and common difference d.
- Calculate to obtain the cumulative sum.
Capabilities and scope
It uses the closed-form arithmetic-series formula rather than adding terms one by one.
How it works
It uses S_n = n/2 × [2a + (n−1)d].
Example
Summing 10 terms starting at 1 with difference 1 gives 55.
Useful for
- Total a plan that increases by a fixed amount each period
- Find the total of an arithmetic progression efficiently
Before you use it
- n should represent a non-negative integer count of terms.
Frequently asked questions
What happens when the common difference is zero?
Every term equals the first term, so the sum becomes n×a.