Math calculators

Sequences and series

Nth term and sum of arithmetic and geometric sequences, infinite geometric series and exact Fibonacci numbers.

Inputs

First term a₁Common difference dTerm number nTerms to list

Results

Methodology

Conventions

Terms are counted from 1. Fibonacci numbers start F₁ = F₂ = 1 and are computed exactly for any n up to 10,000.
An infinite geometric series converges only when |r| < 1.

References

Graham, Knuth and Patashnik, Concrete Mathematics, 2nd ed. (1994)

Formulas

Arithmetic: a_n = a_1 + (n - 1)d,\quad S_n = \tfrac{n}{2}(2a_1 + (n - 1)d)
Geometric: a_n = a_1 r^{n - 1},\quad S_n = a_1\frac{1 - r^n}{1 - r}
Infinite geometric: S_\infty = \frac{a_1}{1 - r},\ |r| < 1
Fibonacci: F_n = F_{n-1} + F_{n-2}