Sequence Calculator

Generate arithmetic and geometric sequences

How to Use This Calculator

1

Select Sequence Type

Choose between arithmetic or geometric sequence.

2

Enter Values

Input the first term, common difference/ratio, and number of terms to generate.

3

Generate Sequence

Click "Generate Sequence" to see the complete sequence displayed.

Formulas

Arithmetic: a_n = a₁ + (n-1)d

where d is the common difference

Geometric: a_n = a₁ × rⁿ⁻¹

where r is the common ratio

Example 1: Arithmetic sequence starting at 2 with difference 3

a₁ = 2, d = 3, n = 5

Sequence: 2, 5, 8, 11, 14

Example 2: Geometric sequence starting at 2 with ratio 3

a₁ = 2, r = 3, n = 5

Sequence: 2, 6, 18, 54, 162

About Sequence Calculator

The sequence calculator generates arithmetic and geometric sequences. An arithmetic sequence adds a constant difference to each term, while a geometric sequence multiplies each term by a constant ratio.

Arithmetic Sequences

  • Each term increases (or decreases) by a constant amount
  • Example: 2, 5, 8, 11, 14, ... (difference = 3)
  • Common applications: linear patterns, regular intervals

Geometric Sequences

  • Each term is multiplied by a constant ratio
  • Example: 2, 6, 18, 54, 162, ... (ratio = 3)
  • Common applications: exponential growth, compound interest

Frequently Asked Questions

What's the difference between arithmetic and geometric sequences?

Arithmetic sequences add a constant difference, while geometric sequences multiply by a constant ratio.

Can I generate sequences with negative values?

Yes! Negative first terms or negative common differences/ratios create sequences with negative terms.

What's the maximum number of terms I can generate?

The calculator limits to 100 terms for display purposes. Very large sequences may be truncated.

Can I use decimals?

Yes! Both the first term and common difference/ratio can be any real numbers, including decimals.

How do I find a specific term in the sequence?

Generate the sequence and count to find the position. Or use the arithmetic/geometric sequence calculators for specific terms.