Home » Math & Conversions » Algebra » Sequence Calculator Sequence Calculator Analyze any number sequence to find the formula, next terms, and sum. Our tool automatically detects Arithmetic, Geometric, and Quadratic sequences. Enter Your Number Sequence: Enter at least 3 numbers, separated by commas or spaces. Analyze Sequence How to Find the Rule for a Sequence This calculator is a powerful tool that automatically checks for the most common types of mathematical sequences. Here are the formulas it uses: 1. Arithmetic Sequence A sequence is arithmetic if the difference between terms is constant. This is called the "common difference" (d). Example: 5, 8, 11, 14... (The common difference `d` is 3). Explicit Formula (nth term): `aₙ = a₁ + (n-1)d` Sum Formula (Series): `Sₙ = n/2 * (2a₁ + (n-1)d)` 2. Geometric Sequence A sequence is geometric if the ratio between terms is constant. This is called the "common ratio" (r). Example: 3, 6, 12, 24... (The common ratio `r` is 2). Explicit Formula (nth term): `aₙ = a₁ * rⁿ⁻¹` Sum Formula (Series): `Sₙ = a₁ * (1 - rⁿ)

Subcategories in Home » Math & Conversions » Algebra » Sequence Calculator Sequence Calculator Analyze any number sequence to find the formula, next terms, and sum. Our tool automatically detects **Arithmetic**, **Geometric**, and **Quadratic** sequences. Enter Your Number Sequence: Enter at least 3 numbers, separated by commas or spaces. Analyze Sequence How to Find the Rule for a Sequence This calculator is a powerful tool that automatically checks for the most common types of mathematical sequences. Here are the formulas it uses: 1. Arithmetic Sequence A sequence is **arithmetic** if the difference between terms is constant. This is called the "common difference" (d). Example: 5, 8, 11, 14... (The common difference `d` is 3). Explicit Formula (nth term): `aₙ = a₁ + (n-1)d` Sum Formula (Series): `Sₙ = n/2 * (2a₁ + (n-1)d)` 2. Geometric Sequence A sequence is **geometric** if the ratio between terms is constant. This is called the "common ratio" (r). Example: 3, 6, 12, 24... (The common ratio `r` is 2). Explicit Formula (nth term): `aₙ = a₁ * rⁿ⁻¹` Sum Formula (Series): `Sₙ = a₁ * (1 - rⁿ).

(1 - r)` 3. Quadratic Sequence A sequence is **quadratic** if the *second* difference (the difference between the differences) is constant. The formula is in the form of a quadratic equation. Example: 1, 4, 9, 16... (The sequence of perfect squares). Explicit Formula (nth term): `aₙ = An² + Bn + C` Frequently Asked Questions (FAQ) What is the difference between an arithmetic and geometric sequence? An **arithmetic** sequence has a *common difference* (you add or subtract the same number each time). A **geometric** sequence has a *common ratio* (you multiply or divide by the same number each time). Is the Fibonacci sequence (1, 1, 2, 3, 5) arithmetic or geometric? Neither. The Fibonacci sequence is a **recursive** sequence, where the next term is the sum of the two preceding ones. It does not have a constant difference (1-1=0, 2-1=1) or a constant ratio (2/1=2, 3/2=1.5). Our calculator does not currently detect recursive sequences like Fibonacci. Related Calculators function Matrix roots logarithm mode range distance formula fibonacci axis of symmetry coordinate

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