Informally, a sequence is just a list of things. For example,

We tend to write the $n^{\text{th}}$ term using the notation $u_n.$ So, we can write:

• $u_1=10$ is the $1^{\text{st}}$ term

• $u_2=13$ is the $2^{\text{nd}}$ term

• $u_3=16$ is the $3^{\text{rd}}$ term

and so on.

There is a definite pattern in the sequence $10,13,16,19,\dots$ We are adding $3$ each time. In fact, this sequence can be given by an explicit formula:

We can check, for example, that

To be precise, we could say that a sequence is a function whose domain is the natural numbers, $\mathbb{N}.$

A sequence is given by the formula

1. Find the first $4$ terms in the sequence

2. Where in the sequence does $44$ appear?

3. Prove that $258$ does not appear in the sequence.