Note the sequence of years in which the Olympics were held, starting in 1996:

**(1996, 2000, 2004, 2008, 2012, 2016… )**

The parentheses suggest that we are working with a set of numbers placed in a certain order. These elements are called sequence terms. Usually each term of a sequence is represented by any letter, usually** The**, accompanied by an index that gives its position or order.

For example, following **(1996, 2000, 2004, 2008,… ),** we have:

- first term = =
**1996**; - second term = =
**2000**; - third term = =
**2004**; - fourth term = =
**2008**; - … (and so on).

The nth term can represent any term in the sequence. For example, if **n = 50**we have and we are referring to **50th term** of the sequence.

## Sequence Definition

Mathematically, sequence is called any function **f** whose domain is .

**Example**

defined by **f (n) = 2n**

Replacing Yourself **no** by natural numbers **1, 2, 3,… ** we have:

Therefore, the sequence can be written as **(2, 4, 6,…, 2n,…)**.

Note that there is a **training law** of the terms of a sequence. From now on, we will study two different ways of defining a sequence: by the general term and by recurrence.

### Sequence defined by the general term

Each term is calculated as a function of your position **no** in sequence.

**Example**

The first three terms of the sequence whose general term isare:

So the sequence that has as its general term , é .

### Sequence defined by recurrence

Each term in the sequence is calculated against the previous term.

**Example**

In the sequence defined by on what, each term except the first is the same as the previous one added to **3**.

Therefore, the sequence can be written as **(4, 7, 10, 13,… )**.