How do I use the Sequence Calculator calculator?

Enter your numerical input and select desired units to get instant accurate results.

How accurate are the conversions?

Conversions use official ISO conversion factors for maximum precision.

Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.

No, all calculations execute 100% locally in your browser with zero data logging.

Yes, it provides reliable estimates for construction, crafting, science, and everyday math.

The calculator will display a friendly error prompt if non-numeric values are entered.

Calculated using standard mathematical and industry formulas.

Free online Sequence Calculator calculator and unit conversion tool for everyday, engineering, and home projects.

Select arithmetic (constant difference) or geometric (constant ratio).
Enter the first term a₁ and the common difference d or ratio r.
Enter the term position n and read aₙ, the partial sum Sₙ, and a sequence preview.
For geometric sequences with |r| < 1, the sum to infinity S∞ is also shown.

nth term and partial sum formulas

Arithmetic: aₙ = a₁ + (n−1)d · Sₙ = n(a₁+aₙ)/2 · Geometric: aₙ = a₁ × rⁿ⁻¹ · Sₙ = a₁(1−rⁿ)/(1−r) · S∞ = a₁/(1−r) if |r|<1

a₁ = first term, d = common difference, r = common ratio, n = term position.

Arithmetic a₁=2, d=3, n=10: a₁₀ = 2 + 9×3 = 29, S₁₀ = 10×(2+29)/2 = 155.

Arithmetic sequences: each term adds a constant. Sequence 2, 5, 8, 11, … has d = 3.
Geometric sequences: each term multiplies by a constant. Sequence 2, 6, 18, 54, … has r = 3.
Gauss's trick: the sum of an arithmetic sequence from 1 to n is n(n+1)/2.
A geometric series with |r| < 1 converges to S∞ = a₁ / (1 − r).

Arithmetic sequences grow linearly (constant addition). Geometric sequences grow exponentially (constant multiplication).

Only converges for geometric sequences with |r| < 1. Example: 1 + 0.5 + 0.25 + … = 2.

How do I use the Sequence Calculator calculator?: Enter your numerical input and select desired units to get instant accurate results.
How accurate are the conversions?: Conversions use official ISO conversion factors for maximum precision.
Does it convert metric and imperial units?: Yes, seamless conversions between metric (meters, kg) and imperial (feet, lbs) are supported.
Is my data stored?: No, all calculations execute 100% locally in your browser with zero data logging.
Can I use this for DIY or engineering projects?: Yes, it provides reliable estimates for construction, crafting, science, and everyday math.
What if I enter invalid inputs?: The calculator will display a friendly error prompt if non-numeric values are entered.

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Note: JavaScript is required for live interactive calculations. Published formulas and reference content remain fully accessible above.