N^th term of an arithmetic or geometric sequence

The main purpose of this calculator is to find expression for the n^th term of a given sequence. Also, it can identify if the sequence is arithmetic or geometric. The calculator will generate all the work with detailed explanation.

N^th term of an arithmetic and geometric sequence

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Select what you have:

Input first few terms of a sequence

Example:

2, 3, 9/2, 27/4

Input general term of a sequence

$ a_n = $

Example:

2n + 1/n

Choose what to compute:

Find expression for the nth term (default)

Identify sequence

Find next term

Find first terms

Find th term

Hide steps

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examples

example 1:ex 1:

Determine if a sequence is arithmetic or geometric : $ 1, 2, 4, 8, ... $.

example 2:ex 2:

What is the next term in the following sequence : $ 1, 5, 9, 13, ... $

example 3:ex 3:

What is the value of x? $$ \frac{2}{3}, 1, \frac{3}{2}, \frac{9}{4}, x $$

example 4:ex 4:

What is the $n^{th}$ term of the sequence? $$ 2, 6, 10, 14, 18, ...$$

example 5:ex 5:

Find the general expression for the arithmetic sequence? $$ \frac{5}{2}, 5, 10, 20, . . . $$

example 6:ex 6:

Find the first five terms of the sequence where $ a_n = 2 n^2 - \dfrac{1}{n} $.

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Arithmetic sequences calculator

Geometric sequences calculator

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Nth term of an arithmetic or geometric sequence