What Is a Number Sequence Calculator?
This calculator generates arithmetic sequences (constant difference between terms) or geometric sequences (constant ratio between terms), showing every term along with the nth term formula result and the sum of the sequence.
How to Use the Number Sequence Calculator
- Choose arithmetic or geometric sequence.
- Enter the first term and common difference (or ratio).
- Enter how many terms to generate.
Sequence Formulas
Worked Example
Sequence: 3, 8, 13, 18, 23, 28, 33, 38, 43, 48
10th term: 3 + (10−1)×5 = 48
Sum of 10 terms: 10/2 × (2×3 + 9×5) = 5 × 51 = 255
Understanding Your Results
An arithmetic sequence adds the same amount each step. A geometric sequence multiplies by the same ratio each step, which can grow (or shrink) much faster than arithmetic sequences over many terms.
Common Mistakes to Avoid
- Confusing arithmetic (constant addition) with geometric (constant multiplication) sequences.
- Using a ratio of 0 or 1 in geometric sequences without expecting a constant or zero sequence.
Frequently Asked Questions
Arithmetic sequences add a constant difference between terms. Geometric sequences multiply by a constant ratio between terms, which typically grows much faster.
Use aₙ = a₁ + (n−1)d, where a₁ is the first term, d is the common difference, and n is the term number you want.
Use Sₙ = n/2 × (2a₁ + (n−1)d), or equivalently, n times the average of the first and last terms.
Yes — a negative ratio produces a sequence that alternates between positive and negative values.
The sequence values shrink toward zero with each term, rather than growing, since each term is smaller than the previous one.