Math CalculatorsClient-Side Calculation Engine

Number Sequence Calculator

Calculate arithmetic and geometric sequence terms and sum.

Math Calculators

Number Sequence Calculator

Calculate arithmetic and geometric sequence terms, the nth term value, and the sum of n terms.

Sequence Terms
2, 7, 12, 17, 22, 27, 32, 37, 42, 47
Nth Term (a_10): 47 | Sum (S_10): 245

What is the Number Sequence Calculator and How Does It Work?

The Number Sequence Calculator generates arithmetic sequences (where each term adds a constant difference) or geometric sequences (where each term multiplies by a constant ratio), and calculates the nth term and the sum of all generated terms.

Calculation Formula
Arithmetic: aₙ = a₁ + (n−1)d | Geometric: aₙ = a₁ × r^(n−1)

For an arithmetic sequence, each term adds a fixed common difference (d) to the previous term. For a geometric sequence, each term multiplies the previous term by a fixed common ratio (r).

Where:
a₁= The first term of the sequence
d or r= The common difference (arithmetic) or common ratio (geometric)
n= The number of terms to generate
Worked Calculation Examples
Arithmetic Sequence
Input:First term=2, Common difference=5, Terms=10
Output:2, 7, 12, 17, 22, 27, 32, 37, 42, 47

Each term adds 5 to the previous one; the 10th term is 2 + (10-1)×5 = 47.

Geometric Sequence
Input:First term=3, Common ratio=2, Terms=5
Output:3, 6, 12, 24, 48

Each term doubles the previous one; the 5th term is 3 × 2⁴ = 48.

Common Real-World Use Cases

Algebra Homework

Verify arithmetic or geometric sequence terms and sums for classroom assignments.

Finance & Growth Modeling

Model compounding growth patterns (geometric) or fixed-increment savings plans (arithmetic).

Pattern Recognition

Extend a numeric pattern to see what comes next and confirm the underlying rule.

How to Use the Number Sequence Calculator
  1. 1Choose arithmetic or geometric sequence type.
  2. 2Enter the first term and the common difference (arithmetic) or common ratio (geometric).
  3. 3Set how many terms to generate.
  4. 4View the full term list, the nth term value, and the sum of all generated terms.
Pro Tips & Suggestions
  • •A common ratio between -1 and 1 (exclusive of 0) produces a geometric sequence that shrinks toward zero.
  • •A common difference of 0 produces a constant sequence where every term equals the first term.

Frequently Asked Questions

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