Mathematics

Number Sequences

Calculate the nth term, sum and first terms of arithmetic or geometric progressions.

01Input and settings

The calculation runs in your browser. You can use the tool without installing software.

02Result

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Enter your values or load the example to see the result here.

About this tool: Number Sequences

Calculate the nth term, sum and first terms of arithmetic or geometric progressions.

In an arithmetic progression, the difference between consecutive terms is constant. In a geometric progression, each term is multiplied by a constant ratio. The tool returns the requested term and the sum of the first n terms; a preview lists up to 24 terms.

How the calculation works

aₙ = a₁+(n−1)d; Sₙ = n(a₁+aₙ)/2; geometric: aₙ = a₁qⁿ⁻¹

Worked example

Mode
Arithmetic
First term
2
Difference / ratio
3
n
5
a₅ = 14; S₅ = 40; 2, 5, 8, 11, 14

Questions and answers

What does this tool do?

Calculate the nth term, sum and first terms of arithmetic or geometric progressions. In an arithmetic progression, the difference between consecutive terms is constant. In a geometric progression, each term is multiplied by a constant ratio. The tool returns the requested term and the sum of the first n terms; a preview lists up to 24 terms.

What affects precision and input format?

Floating-point results are rounded for display. Keep the units shown in the input labels; decimal points and decimal commas are accepted.

Where are the calculations performed?

The calculation runs in your browser. You can use the tool without installing software.

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