Sequence & Series Calculator
Calculate nth term and sum of arithmetic or geometric sequences.
Arithmetic Sequence
Constant difference
Geometric Sequence
Constant ratio
nth Term (aₙ)
—
Sum (Sₙ)
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Arithmetic Sequences
An arithmetic sequence has a constant difference between consecutive terms.
aₙ = a₁ + (n−1)d
Sₙ = n(a₁ + aₙ)/2 = n[2a₁ + (n−1)d]/2
Geometric Sequences
A geometric sequence has a constant ratio between consecutive terms.
aₙ = a₁ · r^(n−1)
Sₙ = a₁(rⁿ − 1)/(r − 1) for r ≠ 1
Examples
| Type | First terms | 10th term | Sum of 10 |
|---|---|---|---|
| Arithmetic (d=3) | 2, 5, 8, 11, ... | 29 | 155 |
| Geometric (r=2) | 2, 4, 8, 16, ... | 1024 | 2046 |
Frequently Asked Questions
What is the difference between a sequence and a series?
A sequence is an ordered list of numbers. A series is the sum of the terms of a sequence. For example, 1, 2, 3, 4, ... is a sequence, while 1 + 2 + 3 + 4 + ... is a series.