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

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

**
Example 1:
**

In the sequence
$2,6,18,54,\mathrm{...}$
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 ${n}^{\text{th}}$ 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: ${a}_{2}={2}^{2}=4$

Fifteenth term: ${a}_{15}={15}^{2}=225$

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