What is an arithmetic series?

An arithmetic series is the sum of all terms in an arithmetic sequence. For example, 2 + 5 + 8 + 11 + 14 is an arithmetic series with first term 2, common difference 3, and 5 terms.

What formula does this calculator use?

It uses S = n/2 × (2a + (n−1)d), where n is the number of terms, a is the first term, and d is the common difference. An equivalent form is S = n/2 × (a + l), where l is the last term.

Can the common difference be negative?

Yes. A negative common difference means the sequence is decreasing. For example, 10, 7, 4, 1, −2 has d = −3. The formula still applies and the sum can be negative.

Can the common difference be zero?

Yes. When d = 0, every term equals the first term, so the sum is simply n × a.

How is this different from a geometric series?

In a geometric series, each term is multiplied by a constant ratio. In an arithmetic series, a constant value is added. The formulas and behaviors are different.

What is the maximum number of terms supported?

Up to 10,000 terms. For larger values the formula is still accurate; the term-by-term preview is capped at 20 entries for readability.

Arithmetic Series Sum Calculator

Enter the first term, common difference, and number of terms to find the sum of an arithmetic series instantly.

Series Parameters

First term (a)

Common difference (d)

Number of terms (n)

Formula

S = n/2 × (2a + (n−1)d)

S = n/2 × (a + l)

where a = first term, d = common difference, n = number of terms, l = last term.

Sum of Series

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Enter values and click Calculate.

Summary

An arithmetic series is the sum of the terms in an arithmetic sequence, where each term increases or decreases by a constant common difference. This calculator applies the standard formula S = n/2 × (2a + (n−1)d) to find the total sum instantly. It also shows the last term, the nth term formula, and a breakdown of the first few terms so you can verify the result.

How it works

Enter the first term (a) — the starting value of the sequence.
Enter the common difference (d) — the constant added to each term.
Enter the number of terms (n) — how many terms to sum.
The calculator applies S = n/2 × (2a + (n−1)d) and displays the sum.
The last term, nth term formula, and first few terms are shown as verification.

Use cases

Solve homework and exam problems involving arithmetic sequences.
Calculate the total of evenly spaced payments or savings amounts.
Sum consecutive integers or odd/even numbers up to a given count.
Verify manual arithmetic series calculations.
Explore how changing the common difference affects the total sum.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu