Number sequence calculator for arithmetic, geometric and Fibonacci terms
Choose a sequence family and term number. HitEquals reports the requested term, finite sum and a visible run of terms without confusing the term index with the number of steps.
Inputs used by this calculator
Number Sequence Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Sequence type | Arithmetic | Arithmetic · Geometric · Fibonacci | Chooses which Number Sequence Calculator method or unknown the engine evaluates. |
| First term | 1 | -1000000000 to 1000000000 | Supplies the first term quantity used by the published equation or result breakdown. |
| Common difference | 2 | -1000000 to 1000000 | Supplies the common difference quantity used by the published equation or result breakdown. |
| Common ratio | 2 | -1000 to 1000 | Supplies the common ratio quantity used by the published equation or result breakdown. |
| Term number (n) | 10 | 1 to 1000 | Supplies the term number (n) quantity used by the published equation or result breakdown. |
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 are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.