Number Sequence Calculator
Calculate arithmetic and geometric sequences — find the nth term, sum, and list the first terms.
About Number Sequences
A number sequence is an ordered list of numbers following a pattern. The two most fundamental types are arithmetic sequences (constant difference between terms) and geometric sequences (constant ratio between terms). These sequences appear throughout mathematics, science, finance, and nature.
Arithmetic Sequences
In an arithmetic sequence with first term a₁ and common difference d, the nth term is aₙ = a₁ + (n−1)d, and the sum of the first n terms is Sₙ = n/2 × (2a₁ + (n−1)d). Examples include counting (1, 2, 3, ...), even numbers (2, 4, 6, ...), and debt payoff schedules.
Geometric Sequences
In a geometric sequence with first term a₁ and common ratio r, the nth term is aₙ = a₁ × r^(n−1), and the sum is Sₙ = a₁(1−rⁿ)/(1−r) for r ≠ 1. Geometric sequences model exponential growth and decay — compound interest, population growth, radioactive decay, and computer memory all follow geometric patterns.
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For a related calculation, use Binary Calculator to convert between binary, decimal, octal, and hexadecimal. Perform binary arithmetic with step-by-step working. Alternatively, use Big Number Calculator to add, subtract, and multiply arbitrarily large integers using JavaScript BigInt. Perfect for 100+ digit numbers.
For the underlying method, read Binary and Hexadecimal Explained: A Beginner's Guide.