Sequence Calculator
Generate arithmetic and geometric sequences
How to Use This Calculator
Select Sequence Type
Choose between arithmetic or geometric sequence.
Enter Values
Input the first term, common difference/ratio, and number of terms to generate.
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.