Arithmetic Series Sum Calculator
Sum of the first n terms of an arithmetic sequence.
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ⓘ Live results
Results
- Sum of series
- 255
- Last term (a_n)
- 48
- Number of terms
- 10
Quick answer
The sum of an arithmetic series is n/2 times the sum of the first and last terms.
S_n = n/2 * (2a + (n-1)d)
How to use the Arithmetic Series Sum Calculator
- 1Enter the first term and the common difference between terms.
- 2Enter how many terms to sum.
- 3The formula multiplies the average of the first and last term by the count.
Worked example
Using the values the calculator loads with:
Inputs
- First term a13
- Common difference d5
- Number of terms n10
Results
- Sum of series255
- Last term (a_n)48
- Number of terms10
Frequently asked questions
What if d is negative?
The sequence decreases, and the formula still works unchanged.
How do I find just the nth term?
Use a + (n-1)d without the summation.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.