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Finding the $n^{th}$ Term of a Sequence

The $n^{th}$ (or general) term of a sequence is usually denoted by the symbol $a_{n}$ .

Example 1:

In the sequence $2, 6, 18, 54, ...$ the first term is
$a_{1} = 2$ , the second term is $a_{2} = 6$ and so forth.

A term is multiplied by $3$ to get the next term.

If you know the formula for the $n^{th}$ term of a sequence in terms of $n$ , then you can find any term.

Example 2:

$a_{n} = n^{2}$

First term: $a_{1} = 1^{2} = 1$

Second term: $a_{2} = 2^{2} = 4$

Math diagram

Fifteenth term: $a_{15} = 15^{2} = 225$

See also $n^{th}$ term of a arithmetic sequence and $n$ ^th term of a geometric sequence .

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