Online Arithmetic and Geometric Sequence Calculator

What Is This Tool?

The Sequence Calculator builds arithmetic, geometric, and Fibonacci sequences and reports the nth term and the sum of the first n terms. Enter the starting values and how many terms you want, and it lists the sequence and the key results. For example, an arithmetic sequence starting at 2 with a common difference of 5 gives 2, 7, 12, 17, …, a 20th term of 97, and a sum of 990.

How to Use This Tool?

• Choose arithmetic, geometric, or Fibonacci.
• Enter the first term and the common difference or ratio.
• Enter how many terms you want.
• Click Calculate to see the sequence, nth term, and sum.

Key Features

• Supports arithmetic, geometric, and Fibonacci sequences.
• Finds the nth term directly with the right formula.
• Computes the sum of the first n terms.
• Lists the opening terms of the sequence.
• Returns exact values for whole-number inputs.

Examples

• Arithmetic with first term 2 and difference 5 gives 2, 7, 12, 17, …
• The 20th term of that sequence is 97, and the sum of 20 terms is 990.
• Geometric with first term 2 and ratio 5 gives 2, 10, 50, 250, …
• The Fibonacci sequence begins 1, 1, 2, 3, 5, 8, and its 10th term is 55.

Common Use Cases

• Solving sequence and series problems in algebra.
• Finding a distant term without listing them all.
• Calculating the sum of many terms quickly.
• Exploring growth patterns and ratios.
• Checking maths homework on sequences.

Tips & Best Practices

• Use a common difference for arithmetic and a common ratio for geometric.
• A negative difference or a ratio below one makes a sequence decrease.
• Whole-number inputs give exact, full-precision results.
• Pick the number of terms carefully, as geometric sequences grow fast.
• The first listed term is the starting value you entered.

Limitations

• Geometric and Fibonacci sequences are limited to a maximum number of terms.
• Decimal inputs are calculated with standard floating-point precision.
• Very large results are shown in shortened scientific form.
• It generates one sequence at a time.

Frequently Asked Questions

What is the difference between arithmetic and geometric sequences?

An arithmetic sequence adds a fixed common difference between terms, while a geometric sequence multiplies by a fixed common ratio.

How is the nth term found?

For arithmetic it is a₁ + (n − 1)d, and for geometric it is a₁ × rⁿ⁻¹, where d is the difference and r is the ratio.

What is the Fibonacci sequence?

Each Fibonacci term is the sum of the two before it, starting 1, 1, 2, 3, 5, 8, and so on.

How is the sum of a sequence calculated?

Arithmetic uses Sₙ = n(2a₁ + (n − 1)d) ÷ 2, and geometric uses Sₙ = a₁(rⁿ − 1) ÷ (r − 1) when the ratio is not 1.

Key Terminology

Arithmetic sequence

A sequence where each term differs from the last by a fixed amount.

Geometric sequence

A sequence where each term is the previous one multiplied by a fixed ratio.

Fibonacci sequence

A sequence where each term is the sum of the two preceding terms.

Common difference

The fixed amount added between terms in an arithmetic sequence.

Common ratio

The fixed multiplier between terms in a geometric sequence.

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