How do you calculate the nth term?

Use the formula an = a1 + (n - 1)d, where a1 is the first term, n is the term position and d is the common difference.

How do you calculate the sum of an arithmetic sequence?

Use Sn = n/2 multiplied by 2a1 + (n - 1)d, or Sn = n(a1 + an)/2.

Free Sequence Calculation Tool

Arithmetic Sequence Calculator

Calculate the nth term, sum of the first n terms and generated values of any arithmetic sequence with complete formulas and instant results.

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Arithmetic Sequence Calculator

Enter the first term, common difference and term position

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Nth term formula aₙ = a₁ + (n − 1)d

Sequence sum formula Sₙ = n ÷ 2 [2a₁ + (n − 1)d]

First Term a₁

The starting value of the arithmetic sequence.

Common Difference d

The constant amount added between terms.

Term Number n

The position and number of terms to calculate.

Nth Term

Value of the requested term.

Sum of Terms

Total of the first requested terms.

Generated Sequence

Your generated sequence will appear here.

Nth term calculation aₙ = a₁ + (n − 1)d

Sum calculation Sₙ = n ÷ 2 [2a₁ + (n − 1)d]

Try an example

What Is an Arithmetic Sequence Calculator?

An arithmetic sequence calculator finds values in a number pattern where the same amount is added to or subtracted from every consecutive term. This fixed amount is called the common difference.

Enter the first term, common difference and required term number to calculate the nth term, the total of the first n terms and a preview of the complete sequence.

The calculator supports positive numbers, negative numbers, decimals, increasing sequences and decreasing sequences.

Nth term calculation Find the value at any specified position in the sequence.

Arithmetic series sum Calculate the total of the first n sequence terms.

Sequence generator View up to the first 20 generated terms for easier checking.

Arithmetic Sequence Formulas

These formulas are used to calculate individual terms and the total of a finite arithmetic sequence.

Nth term aₙ = a₁ + (n − 1)d

Sum using first term Sₙ = n/2 [2a₁ + (n − 1)d]

Sum using endpoints Sₙ = n(a₁ + aₙ)/2

Common difference d = aₙ − aₙ₋₁

Simple Process

How the Arithmetic Sequence Calculator Works

Calculate a complete arithmetic sequence in three simple steps.

Enter the First Term

Add the starting number of the sequence. This value is represented by a₁ in the formulas.

Add the Common Difference

Enter the constant number added between consecutive terms. Use a negative value for decreasing sequences.

Choose the Term Number

Enter the required position and calculate the nth term, sequence sum and generated values instantly.

Formula Guide

Arithmetic Sequence Formulas Explained

Understand the formulas used to find a particular term and calculate the total of an arithmetic series.

Nth Term Formula

The nth term formula calculates the value located at a particular position in an arithmetic sequence.

aₙ = a₁ + (n − 1)d

aₙ The value of the required term
a₁ The first term of the sequence
n The position of the required term
d The common difference between terms

Sum Formula

The sum formula calculates the total obtained by adding the first n terms of an arithmetic sequence.

Sₙ = n/2 [2a₁ + (n − 1)d]

Sₙ The total of the first n terms
n The number of terms being added
a₁ The first term in the sequence
d The constant common difference

Worked Examples

Arithmetic Sequence Examples

Compare common arithmetic sequences and their calculated results.

First Term	Difference	Term Number	Nth Term	Sum	Sequence Preview
3	5	10	48	255	3, 8, 13, 18, 23...
20	−3	8	−1	76	20, 17, 14, 11, 8...
5	4	6	25	90	5, 9, 13, 17, 21, 25
0.5	1.5	5	6.5	17.5	0.5, 2, 3.5, 5, 6.5
12	0	5	12	60	12, 12, 12, 12, 12

Helpful Answers

Arithmetic Sequence Calculator FAQs

Find answers to common questions about arithmetic sequences, terms and sums.

What is an arithmetic sequence?

An arithmetic sequence is a list of numbers in which the difference between consecutive terms is always the same. For example, 3, 7, 11, 15 has a common difference of 4.

How do I find the nth term?

Use aₙ = a₁ + (n − 1)d. Multiply the common difference by one less than the term position and then add the first term.

How do I find the common difference?

Subtract one term from the term immediately after it. For example, in 8, 13, 18, the common difference is 13 − 8 = 5.

Can the common difference be negative?

Yes. A negative common difference creates a decreasing arithmetic sequence. For example, 20, 17, 14 and 11 has a common difference of −3.

Can an arithmetic sequence use decimals?

Yes. Both the first term and common difference may contain decimal values. The calculator supports positive decimals and negative decimals.

What happens when the common difference is zero?

Every term remains equal to the first term. For example, when a₁ is 7 and d is 0, the sequence is 7, 7, 7, 7 and so on.

What is the difference between a sequence and a series?

A sequence is an ordered list of terms. A series is the result of adding those terms together. This calculator provides both the sequence values and their sum.

Calculate Any Arithmetic Sequence Instantly

Enter your values above to find the nth term, total sum and generated sequence with a complete formula breakdown.

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