A walkthrough, end to end.
- 1
Pick sequence type: arithmetic (constant difference) or geometric (constant ratio).
- 2
Enter the first term, the common difference (or ratio), and the number of terms.
- 3
The calculator generates the sequence, finds the n-th term, and computes the sum.
Sequence formulas
Arithmetic: aₙ = a₁ + (n−1)d. Sum Sₙ = n(a₁ + aₙ)/2. Geometric: aₙ = a₁ · r^(n−1). Sum Sₙ = a₁(1−rⁿ)/(1−r), or n·a₁ if r = 1.
What you can do with this.
Arithmetic sequence (constant difference)
5, 8, 11, 14, … with a₁=5, d=3. The calculator generates the sequence and computes any n-th term + sum.
Geometric sequence (constant ratio)
2, 6, 18, 54, … with a₁=2, r=3. The calculator handles geometric progressions including fractional / negative ratios.
Compound interest as geometric
Money compounds geometrically. $1,000 at 7%/yr: 1000, 1070, 1144.90, 1225.04, … (a₁=1000, r=1.07). The calculator confirms compound growth math.
Salary raises
Annual 4% raise on $60K salary: 60000, 62400, 64896, … geometric with r=1.04. After 10 years: a₁₀ = 60000 × 1.04⁹ ≈ $85,400.
Fibonacci-like (recurrence)
Fibonacci: 0, 1, 1, 2, 3, 5, 8, … is NOT arithmetic or geometric. The calculator handles only constant-difference or constant-ratio sequences.
Series sum
Sum of first 100 positive integers: 1+2+…+100 = 5050 (arithmetic with a₁=1, d=1, n=100). Calculator confirms the formula instantly.
Geometric infinite sum
If |r| < 1: lim Sₙ = a₁ / (1−r). e.g., 1 + 0.5 + 0.25 + 0.125 + … = 2. The calculator handles finite n; infinite sum requires |r| < 1.
Sequence calculator 2026 — what's current
Foundational pre-calculus / discrete math. AI tools handle reliably. Calculator wins for instant generation and verification.
Frequently asked.
If consecutive differences are constant → arithmetic. If consecutive ratios are constant → geometric. Some sequences (Fibonacci, prime numbers) are neither.
n ≥ 1 typically. For n=1, sequence is just a₁; sum is a₁. Calculator handles these edge cases.
Then it's actually a constant sequence (or trivially arithmetic with d=0). Sum = n·a₁. Calculator handles this special case.
No. Calculations run entirely in your browser.