Math & Algebra Tool

Number Sequence Generator

Generate Arithmetic and Geometric progressions.

Σ The Formula

Arithmetic: a\u2099 = a\u2081 + (n-1)d | Geometric: a\u2099 = a\u2081 \u00d7 r^(n-1)

Real World Examples

Arithmetic
2, 4, 6, 8... (Start=2, Diff=2)
Geometric
3, 6, 12, 24... (Start=3, Ratio=2)
Decreasing
100, 95, 90... (Start=100, Diff=-5)
Alternating
1, -2, 4, -8... (Start=1, Ratio=-2)

# About This Calculator

This tool generates the first 'n' terms of a number sequence. It supports the two most common types: Arithmetic Progressions (AP) and Geometric Progressions (GP).

Arithmetic Sequence: Each term is found by adding a constant "common difference" to the previous term (e.g., 2, 4, 6, 8...). Used in simple interest and linear growth.

Geometric Sequence: Each term is found by multiplying the previous term by a constant "common ratio" (e.g., 2, 4, 8, 16...). Used in population growth, compound interest, and viral trends.

Simply enter your starting parameters to generate the list and visualize how the sequence grows (or shrinks).

How To Use

  1. Choose Arithmetic (+) or Geometric (×).
  2. Enter Start Value (a₁).
  3. Enter Difference/Ratio.
  4. Enter Count (how many numbers).
  5. Click Generate.

Frequently Asked Questions

What is an Arithmetic Progression (AP)?+

A sequence where the difference between consecutive terms is constant. Example: 5, 10, 15, 20 (difference is +5).

What is a Geometric Progression (GP)?+

A sequence where the ratio between consecutive terms is constant. Example: 3, 9, 27, 81 (ratio is ×3).

Can I use negative numbers?+

Yes! A negative difference in AP makes the numbers go down (10, 8, 6). A negative ratio in GP makes numbers alternate signs (2, -4, 8, -16).

What is the Fibonacci sequence?+

It's a special sequence where each number is the sum of the two preceding ones (1, 1, 2, 3, 5...). This tool focuses on AP and GP, but Fibonacci is famous in nature.

How do I find the nth term?+

Arithmetic: a_n = a_1 + (n-1)d. Geometric: a_n = a_1 × r^(n-1). This tool calculates it automatically.

Is Number Sequence Generator free to use?+

Yes, Number Sequence Generator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

This tool generates the first 'n' terms of a number sequence. It supports the two most common types: Arithmetic Progressions (AP) and Geometric Progressions (GP).

Arithmetic Sequence: Each term is found by adding a constant "common difference" to the previous term (e.g., 2, 4, 6, 8...). Used in simple interest and linear growth.

Geometric Sequence: Each term is found by multiplying the previous term by a constant "common ratio" (e.g., 2, 4, 8, 16...). Used in population growth, compound interest, and viral trends.

Simply enter your starting parameters to generate the list and visualize how the sequence grows (or shrinks).

Related Tools

Fraction Calculator

Fraction Simplifier

Fraction to Decimal

Decimal to Fraction