# Sequence Calculator - Arithmetic, Geometric and Fibonacci

> Free online sequence calculator: nth term, sum of n terms, mean and infinite sum for arithmetic and geometric sequences, plus exact big-integer Fibonacci.

- URL: https://qilingtools.com/en/math/sequence
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Enter the first term, the common difference or ratio and how many terms you need to get the nth term, the sum and the full list. Geometric series also give the infinite sum when |r| < 1, and Fibonacci numbers are exact big integers.

## How to use

1. Choose arithmetic, geometric or Fibonacci
2. Enter a₁, the difference d or ratio r, and n
3. Read the nth term and the sum, and copy the full list below

## Features

- Arithmetic: nth term, sum, mean
- Geometric: nth term, sum, infinite sum when it converges
- Fibonacci with BigInt up to the 500th term
- Full list of terms, copyable in one click
- Formulas shown alongside

## FAQ

### What is the sum formula for an arithmetic sequence?

Sₙ = n(a₁+aₙ)/2 with aₙ = a₁ + (n−1)d. Both aₙ and Sₙ are shown.

### When does a geometric series have an infinite sum?

When |r| < 1 it converges to S∞ = a₁/(1−r); when |r| ≥ 1 it diverges and the tool says so.

### What is the 100th Fibonacci number?

Enter 100 for n: it is exactly 354224848179261915075, computed with big integers rather than floating point.

### How many terms can it list?

Up to 1000 for arithmetic and geometric sequences and 500 for Fibonacci, all copyable as a list.

### Can I plot the sequence?

Yes. Click “Plot the terms” under the results and the terms are sent to the grapher as a line against their index — an arithmetic sequence comes out as a straight line, a geometric one as an exponential curve.

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