A number sequence is an ordered list following a rule.
About this calculator
A number sequence is an ordered list following a rule. Arithmetic sequences add the same amount each step — like 2, 5, 8, 11 with difference 3. Geometric sequences multiply by a fixed ratio — like 3, 6, 12, 24 with ratio 2. The Fibonacci sequence adds the two previous terms: 1, 1, 2, 3, 5, 8, and so on.
This calculator finds the nth term and the sum of the first n terms for all three types. For arithmetic and geometric sequences you set the first term and either the common difference or ratio. For Fibonacci, the classic definition starts at 1, 1 regardless of other fields.
These formulas appear in savings plans, population models, and exam papers. For powers and roots use the [[exponent]] and [[root]] calculators; for ratios in recipes use the [[ratio]] calculator; for general algebra try the [[quadratic]] equation solver.
Common uses
- Find the 10th term of an arithmetic progression
- Sum the first n terms of a geometric series
- Look up Fibonacci numbers for puzzles or coding
- Verify sequence formulas from school or competitive exams
Frequently asked questions
What is the 10th term of 2, 5, 8, 11, …?
This is arithmetic with a₁ = 2 and d = 3. The 10th term is a₁₀ = 2 + 9×3 = 29. The sum of the first 10 terms is S₁₀ = 10/2 × (4 + 27) = 155.
How do you find the nth term of a geometric sequence?
Use a_n = a₁ × r^(n−1). Example: first term 3, ratio 2, 5th term = 3 × 2⁴ = 48.
What is the 12th Fibonacci number?
Starting 1, 1, 2, 3, 5, 8, … the 12th Fibonacci number is 144. Each term after the second is the sum of the two before it.
When does the geometric series sum formula fail?
When r = 1 the sum is simply n × a₁. When |r| > 1 the nth term grows quickly — check that n is reasonable for display.