Number Sequence Calculator
Find the next term or the formula of an arithmetic and geometric sequence.
Tip: An arithmetic sequence models linear growth (e.g. a salary rising 500 ALL/month), while a geometric sequence models exponential growth (e.g. compound interest).
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About this digital tool
The number sequence calculator finds the n-th term and the sum of the first n terms for an arithmetic or geometric sequence. Choose the type of sequence, enter the first term (a1), the difference d (or the ratio r) and the number of terms n. You get the term, the sum and the formula used.
In an arithmetic sequence the n-th term is a1 + (n − 1) × d and the sum n × (a1 + an) ÷ 2. For a1 = 3, d = 4, n = 5 the terms are 3, 7, 11, 15, 19 and the sum 5 × 22 ÷ 2 = 55. In a geometric sequence an = a1 × r^(n−1) and the sum a1 × (rⁿ − 1) ÷ (r − 1). For a1 = 2, r = 3, n = 4 the terms are 2, 6, 18, 54 and the sum 80. It is used in algebra, finance and exponential growth.
How to use
- Choose the type of sequence (arithmetic or geometric)
- Enter the first term (a₁)
- Enter the difference (d) or the ratio (r)
- Enter n (the term you want)
- See the n-th term and the sum
Frequently asked questions
What is an arithmetic sequence?
A sequence where the difference between two consecutive terms is constant (d). Formula: aₙ = a₁ + (n-1)d. Example: 2, 5, 8, 11, 14... (d = 3).
What is a geometric sequence?
A sequence where the ratio between two consecutive terms is constant (r). Formula: aₙ = a₁ × r^(n-1). Example: 3, 6, 12, 24, 48... (r = 2).
How is the sum of n terms found?
Arithmetic: Sₙ = n/2 × (a₁ + aₙ) = n/2 × (2a₁ + (n-1)d). Geometric: Sₙ = a₁ × (rⁿ - 1) / (r - 1) when r ≠ 1.
How is the n-th term of an arithmetic sequence found?
an = a1 + (n − 1) × d. E.g. for a1 = 2, d = 3, n = 10: a10 = 2 + 9 × 3 = 29, and the sum S10 = 10 × (2 + 29) ÷ 2 = 155.