justyourcalculatorNumber Sequence Calculator
Nth terms and sums for arithmetic, geometric and Fibonacci sequences.
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Number Sequence Calculator
Arithmetic, geometric and Fibonacci sequences
Term 10 (aₙ)
29
Sum of the first 10 terms: 155
- nth term
- 29
- Sum of first 10 terms (Sₙ)
- 155
- Term
How it was calculated
- aₙ = a₁ + (n - 1)d = 2 + (10 - 1) × 3 = 29
- Sₙ = n(a₁ + aₙ) / 2 = 10 × (2 + 29) / 2 = 155
| n | Term | Running sum |
|---|---|---|
| 1 | 2 | 2 |
| 2 | 5 | 7 |
| 3 | 8 | 15 |
| 4 | 11 | 26 |
| 5 | 14 | 40 |
| 6 | 17 | 57 |
| 7 | 20 | 77 |
| 8 | 23 | 100 |
| 9 | 26 | 126 |
| 10 | 29 | 155 |
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How the number sequence calculator works
An arithmetic sequence adds the same amount each time (2, 5, 8, 11, ...). Its nth term is a₁ + (n − 1)d and the sum of the first n terms is n(a₁ + aₙ)/2, the trick Gauss used to add 1 to 100.
A geometric sequence multiplies by the same ratio each time (2, 6, 18, 54, ...). Its nth term is a₁ × rⁿ⁻¹ and the sum of n terms is a₁(1 − rⁿ)/(1 − r). When the ratio is between -1 and 1 the terms shrink and the infinite sum converges to a₁/(1 − r).
In the Fibonacci sequence each term is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, ... Fibonacci numbers are computed exactly, so even F₅₀₀₀ (over 1,000 digits) is correct, and the ratio of neighbors approaches the golden ratio, about 1.618.
Using and checking your result
Published by JustYourCalculator. Check the units and assumptions above, and compare a known example before relying on the output. Calculations use browser arithmetic and may round displayed values.
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