AI Engineering FoundryLoadingโฆ
Loadingโฆ
Find the nth term of an arithmetic or geometric sequence with its explicit and recursive formulas, or paste a few terms to identify the sequence and continue it.
Also covers: Arithmetic sequence calculator ยท Geometric sequence calculator ยท Nth term calculator ยท Common difference ยท Common ratio
Integers, decimals, or fractions like 1/2.
Up to 1,000,000.
Term a10
39
Explicit formula
aโ = 3 + (n โ 1) ร 4
Recursive formula
aโ = aโโโ + 4
aโ = 3
Sum of first 10
210
First 10 terms
3, 7, 11, 15, 19, 23, 27, 31, 35, 39
Working
Give the first term and the common difference or ratio, or paste three or more terms and let the calculator work out the pattern.
Arithmetic sequences add the same amount each time (5, 8, 11, โฆ); geometric sequences multiply by the same amount (2, 6, 18, โฆ).
You get the term you asked for, the explicit and recursive formulas, the first terms, and the working. Fractions stay exact.
Arithmetic: aโ = aโ + (n โ 1)d. Geometric: aโ = aโ ยท rโฟโปยน. Here aโ is the first term, d the common difference, and r the common ratio.
It checks whether every difference between consecutive terms is the same (arithmetic) or every ratio is the same (geometric). With fewer than three terms both are possible, so three or more are needed.
Terms are calculated exactly, and rโฟ grows very fast: 2ยฒโฐโฐโฐ already has 603 digits. Large results are shown in scientific notation.
No. Every calculation runs in your browser.
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