Free Number Sequence Calculator Online
This free online number sequence calculator generates arithmetic, geometric, and Fibonacci sequences with formulas, next terms, and partial sums.
Sequence Parameters
Sequence
Set parameters above
How the Number Sequence Calculator Works
Select a sequence type, enter the starting parameters, and specify how many terms to generate. The number sequence calculator produces the sequence, shows the general formula, computes partial sums, and identifies the nth term. The number sequence calculator supports three fundamental sequence types.
For arithmetic sequences: the number sequence calculator uses a_n = a_1 + (n−1)d, where a_1 is the first term and d is the common difference. Sum = n/2 × (2a_1 + (n−1)d). Enter a_1 = 5, d = 3, and the number sequence calculator gives 5, 8, 11, 14, 17...
For geometric sequences: the number sequence calculator uses a_n = a_1 × r^(n−1). Sum = a_1(1−r^n)/(1−r) for r ≠ 1. The number sequence calculator generates terms and computes partial sums automatically.
Sequence Types
Arithmetic
Constant difference between terms. Formula: a_n = a_1 + (n−1)d. The number sequence calculator shows all terms and sum.
Geometric
Constant ratio between terms. Formula: a_n = a_1 × r^(n−1). The number sequence calculator computes terms and partial sums.
Fibonacci
Each term = sum of two previous. 0, 1, 1, 2, 3, 5, 8... The number sequence calculator generates any length.
Tips for Using the Number Sequence Calculator
Pick the Right Type
Constant difference = arithmetic. Constant ratio = geometric. Sum of previous two = Fibonacci. The number sequence calculator handles all three.
Check the Sum
The number sequence calculator shows the partial sum of generated terms — useful for series problems.
Use the Formula
The number sequence calculator displays the general term formula. Use it to find any specific term without generating the full sequence.
Negative Values Work
The number sequence calculator handles negative first terms, differences, and ratios (including alternating sequences with r < 0).
Frequently Asked Questions
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