Find the nth term and the sum of a sequence.
aₙ = a₁ + (n − 1)d. For 3, 7, 11… the 10th term is 39.
A sequence is an ordered list of numbers that follows a rule. This calculator handles the three most common kinds: arithmetic sequences (add a fixed difference), geometric sequences (multiply by a fixed ratio) and the Fibonacci sequence (each term is the sum of the previous two). For each it gives the nth term, the sum of the first n terms, the opening terms and, for geometric sequences, the sum to infinity when it converges.
Exact Fibonacci numbers are computed with big integers, so F(1000) is correct to every digit. Related: the Exponent Calculator, Average Calculator, Compound Interest Calculator and Big Number Calculator.
The calculator applies the standard method step by step.
| Item | Value |
|---|---|
| nth term (aₙ) | 39 |
| Sum of the first n terms (Sₙ) | 210 |
| First terms | 3, 7, 11, 15, 19, 23, 27, 31, 35, 39 |
| Type | Increasing |
| Term | Value |
|---|---|
| 3, 7, 11… (n = 5) | 19 |
| 3, 7, 11… (n = 10) | 39 |
| 3, 7, 11… (n = 20) | 79 |
| 3, 7, 11… (n = 50) | 199 |
| 3, 7, 11… (n = 100) | 399 |
A sequence where each term differs from the last by a constant, such as 3, 7, 11, 15… (difference 4).
A sequence where each term is the previous one multiplied by a constant ratio, like 2, 6, 18, 54… (ratio 3).
0, 1, 1, 2, 3, 5, 8, 13, 21… where each number is the sum of the two before it.
Sₙ = n × (first + last) ÷ 2. The sum of the first 10 terms of 3, 7, 11… is 210.
Only when the common ratio is between −1 and 1; then the sum is a₁ ÷ (1 − r).
The ratio of consecutive Fibonacci numbers approaches φ ≈ 1.618034.
It uses the standard method: arithmetic aₙ = a₁ + (n − 1)d geometric aₙ = a₁rⁿ⁻¹ Fibonacci F(n) = F(n−1) + F(n−2) The full working and a worked example are shown on this page.
Decimal results use standard double-precision arithmetic (about 15–16 significant digits). Tools that work with whole numbers — big numbers, factors, bases, combinations — use exact integer arithmetic, so no digits are lost.
Yes for checking your work and learning the method. The steps and formula are shown so you can understand the answer, but follow your teacher's rules about calculators in exams.
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