Arithmetic Series Calculator

Use our free arithmetic series calculator to find Sₙ (sum of the first n terms), sum from term m to n, or determine n from a target sum.

Math

Mode

First Term (a₁)

Common Difference (d)

Number of Terms (n)

From Term (m)

Target Sum (Sₙ)

Formula

An arithmetic series is the sum of an arithmetic sequence. The sum Sₙ of the first n terms can be found using Sₙ = (n/2)(a₁ + aₙ) or Sₙ = (n/2)(2a₁ + (n-1)d).

Sₙ = (n/2) × (a₁ + aₙ) = (n/2) × (2a₁ + (n−1)d)

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select a mode.
2Sₙ: enter a₁, d, n.
3Range m..n: enter a₁, d, m, n.
4Find n: enter a₁, d, target Sₙ.
5Click Calculate.

Examples

S₁₀ for 3,5,7,...,21

1.S₁₀ = 10/2 × (3 + 21) = 5 × 24 = 120

Result: 120

Sum terms 5-10

1.a₅=11, a₁₀=21, 6 terms
2.Sum = 6/2 × (11+21) = 96

Result: 96

Find n for sum 120

1.n = (-4 + √(16+1920))/4 = 10

Result: 10

Frequently Asked Questions

The sum of the terms of an arithmetic sequence.

Sₙ = (n/2)(a₁ + aₙ) or Sₙ = (n/2)(2a₁ + (n-1)d).

Sums only terms from position m to n.

Yes, if terms are negative or d is negative.

Rearranged quadratic formula: n = (-(2a₁-d) + √((2a₁-d)²+8dSₙ)) / (2d).

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CalculateMe Team

Last updated: 2026-07-14

Arithmetic Series Calculator

Formula

How It Works

Examples

S₁₀ for 3,5,7,...,21

Sum terms 5-10

Find n for sum 120

Frequently Asked Questions

What is an arithmetic series?

Formula?

What is the range mode?

Can the sum be negative?

Find n from sum?

Related Calculators

Arithmetic Series Calculator

Formula

How It Works

Examples

S₁₀ for 3,5,7,...,21

Sum terms 5-10

Find n for sum 120

Frequently Asked Questions

What is an arithmetic series?

Formula?

What is the range mode?

Can the sum be negative?

Find n from sum?

Related Calculators