Arithmetic Sequence Calculator

Calculate arithmetic sequences, find nth terms, sums, and common differences. Free online arithmetic sequence calculator.

Calculator

Arithmetic Sequence Calculator

Calculate arithmetic sequences, find the nth term, sum of terms, and common difference with our free online calculator. Perfect for mathematics and statistics.

Arithmetic Sequence Calculator

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Sequence Parameters

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Result

Enter sequence parameters above to see the calculation result.

Understanding Arithmetic Sequences

Definition

An arithmetic sequence is a sequence where each term after the first is obtained by adding a constant difference to the preceding term.

Common Difference

The constant difference between consecutive terms. Can be positive, negative, or zero.

Nth Term Formula

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

Sum Formula

Sn = n/2(a₁ + an) or Sn = n/2[2a₁ + (n-1)d], where n is the number of terms.

How to Use

  1. Select what you want to calculate (nth term, sum, etc.)
  2. Enter the first term, common difference, and number of terms
  3. Or enter known terms to find the pattern
  4. Click "Calculate Arithmetic Sequence" to see the result
  5. Review the detailed calculation and sequence

Examples

Sequence: 2, 5, 8, 11, 14, ...

First term: 2, Common difference: 3

10th term: a₁₀ = 2 + (10-1)Ɨ3 = 29

Sum of first 10 terms:

S₁₀ = 10/2(2 + 29) = 5 Ɨ 31 = 155

Finding common difference:

Given terms: 7, 12, 17, 22 → d = 5

Features

  • • Find nth term of sequence
  • • Calculate sum of terms
  • • Find common difference
  • • Generate sequence terms
  • • Work with known terms
  • • Free to use

Perfect For

  • • Mathematics students
  • • Statistics calculations
  • • Financial planning
  • • Pattern recognition
  • • Series and sequences
  • • Mathematical modeling

Frequently Asked Questions

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers where the difference between consecutive terms is constant. This constant difference is called the common difference.

How do I find the nth term of an arithmetic sequence?

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

How do I find the sum of an arithmetic sequence?

Use the formula: Sn = n/2(a₁ + an) or Sn = n/2[2a₁ + (n-1)d], where n is the number of terms.