Nth Term Of A Sequence Calculator

Work out nth term of a sequence instantly with clear inputs, formula shown and shareable results.

About Nth Term Of A Sequence Calculator

An arithmetic sequence adds a fixed difference, giving aₙ = a + (n − 1)d. A geometric sequence multiplies by a fixed ratio, giving aₙ = a·r^(n−1). Both count the first term as n = 1.

Formulas

Arithmetic nth term

aₙ = a + (n − 1)d

Geometric nth term

aₙ = a · r^(n−1)

Worked example

With the default values below, Nth Term Of A Sequence Calculator returns The nth term of 38.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First term: 5
Common difference or ratio: 3
Which term to findaccepts 1–100,000: 12
Sequence typeone of Arithmetic (add the difference), Geometric (multiply by the ratio): Arithmetic (add the difference)

Results

The nth term: 38.00000000
The following term: 41.00000000
General formula: aₙ = 5 + (n - 1) × 3
Type: Arithmetic

Step by step

1Values used
2Arithmetic nth term
3Geometric nth term
4The nth term= 38.00000000
5The following term= 41.00000000
6General formula= aₙ = 5 + (n - 1) × 3
7Type= Arithmetic

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

12th term of 5, 8, 11, …?

5 + 11 × 3 = 38.

Why is it (n − 1) and not n?

Because the first term needs no steps added, so the number of steps to term n is one fewer than n.