# Definition:Term (Algebra)

## Definition

A term is either a variable or a constant.

Let $a \circ b$ be an expression.

Then each of $a$ and $b$ are known as the terms of the expression.

The word term is usually used when the operation $\circ$ is addition, that is $+$.

## Instances

### Term of Fraction

The terms of a fraction are referred to as the Numerator and the Denominator:

### Numerator

The term $a$ is known as the numerator of $\dfrac a b$.

### Denominator

The term $b$ is known as the denominator of $\dfrac a b$.

A helpful mnemonic to remember which goes on top and which goes on the bottom is "Numerator Over Denominator", which deserves a "nod" for being correct.

### Term of Polynomial

Let $P = a_n x^n + a_{n - 1} x^{n - 1} + \cdots + a_1 x + a_0$ be a polynomial.

Each of the expressions $a_i x^i$, for $0 \le i \le n$, is referred to as a term of $P$.

### Term of Sequence

The elements of a sequence are known as its terms.

Let $\sequence {x_n}$ be a sequence.

Then the $k$th term of $\sequence {x_n}$ is the ordered pair $\tuple {k, x_k}$.