Complete guide
Number sequence calculator for arithmetic, geometric and Fibonacci terms
Choose a sequence family and term number. Calculator24 reports the requested term, finite sum and a visible run of terms without confusing the term index with the number of steps.
What a number sequence is
A sequence is an ordered list. Position matters: the same value can appear more than once and still represent different terms.
Arithmetic sequences
Consecutive arithmetic terms have a constant difference d. Their finite sum is the average of the first and last terms multiplied by n.
aₙ=a₁+d(n−1)Sₙ=n(a₁+aₙ)/2Geometric sequences
Each geometric term multiplies the previous term by r. When r is not one, a closed form gives the finite sum.
aₙ=a₁r^(n−1)Sₙ=a₁(1−rⁿ)/(1−r)Fibonacci indexing
This page uses F₀=0 and F₁=1. Because the input asks for n but the first displayed term is F₀, a request for n=10 returns 55.
Worked arithmetic example
Starting at one and adding two creates 1, 3, 5, …, 19. Ten terms sum to 100.
Recognizing limits
Many finite lists can mimic several patterns. A few observed values do not prove a unique generating rule, and an infinite series requires a separate convergence test.
Three supported sequence families
| Family | Change | Example |
|---|---|---|
| Arithmetic | Add d | 1, 3, 5, 7 |
| Geometric | Multiply by r | 1, 2, 4, 8 |
| Fibonacci | Add prior two | 0, 1, 1, 2 |
Frequently asked questions
What is the nth arithmetic term?
It is a₁+d(n−1).
What is the nth geometric term?
It is a₁r^(n−1).
Does Fibonacci start with 0 or 1?
This calculator uses F₀=0 and F₁=1.
Can a common difference be negative?
Yes. The arithmetic sequence then decreases.
Can a common ratio be zero?
Yes. Every term after the first is zero.
Does a finite sum prove an infinite series converges?
No. Infinite-series convergence is a separate question.
What to keep in mind
Displayed lists are limited to the first 100 terms. Very large geometric or Fibonacci requests are rejected when JavaScript cannot represent a finite numeric result.
Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.