What is a Number Sequence Calculator?

A number sequence calculator is a no-cost online calculator that calculates terms of a specified number sequence, the nᵗʰ term (aₙ) of the sequence and the sum of the first n terms (Sₙ) for given inputs. It allows you to select common number pattern outputs, arithmetic sequences (adding a constant difference), geometric sequences (multiplying by a constant ratio), and some famous sequences or series like Fibonacci numbers, or primes. The pattern you choose (sequence) is generated by the calculator. This means you can calculate the nᵗʰ term of a sequence without calculating all of the terms one at a time. The calculator is a great way to get the results quickly, accurately, for homework, exam, or project examples.

How Does the Number Sequence Calculator Work?

1. Choose the type of sequence (arithmetic, geometric, fibonacci, prime, etc.)
2. Fill in all of the required inputs which include first term a₁, common difference d (arithmetic), constant ratio r (geometric), and number of terms n. That is it. If you select fibonacci, just let the calculator know how many terms to generate; for primes, let the calculator know how many primes to generate.
3. Click, calculate and see (1) the terms of your sequence, (2) your nᵗʰ term attained from a calculation of aₙ, and (3) the, if applicable, partial sum Sₙ (aggregation) of your specified number of terms.
4. Copy/Export your results and use them for class assignments, reports, or save/preserve/results.

Formulas Used in Number Sequence Calculator

Arithmetic

• nᵗʰ term: aₙ = a₁ + (n − 1)d
• Sum of first n terms: Sₙ = n/2 · (2a₁ + (n − 1)d) (equivalently, Sₙ = n/2 · (a₁ + aₙ))

Geometric

• nᵗʰ term: aₙ = a₁ · r⁽ⁿ⁻¹⁾
• Sum of first n terms (r ≠ 1): Sₙ = a₁ · (1 − rⁿ)/(1 − r); if r = 1, then Sₙ = n · a₁

Key Benefits of Using This Number Sequence Calculator Online

• Quickly and accurately produce term values and partial sums (Sₙ).
• Generate arithmetic sequences, geometric sequences, Fibonacci sequences and prime sequences
• Generate the nth term and calculate the sum of series -- no manual algebra!
• Easily check results on a mobile device.
• Ideal for classroom and practice work, assessment tasks, coding practice, competitions, and research notes.

Practical Example Use-Case

Arithmetic example: a₁ = 5, d = 3, n = 10.

• nᵗʰ term: a₁₀ = 5 + (10−1)·3 = 5 + 27 = 32
• First 10 terms: 5, 8, 11, 14, 17, 20, 23, 26, 29, 32
• Sum: S₁₀ = 10/2 · (5 + 32) = 5 · 37 = 185

Geometric example: a₁ = 2, r = 3, n = 6.

• a₆ = 2 · 3⁵ = 486; S₆ = 2 · (1 − 3⁶)/(1 − 3) = 728

Fibonacci (first 8 terms): 0, 1, 1, 2, 3, 5, 8, 13