Sequences

A numerical sequence is an ordered list of numbers \((u_0,\,u_1,\,u_2,\dots)\) defined by a rule.

\(n\)	0	1	2	\(\dots\)
\(u_n\)	\(u_0\)	\(u_1\)	\(u_2\)	\(\dots\)

The number \(u_n\) is called the \(n\)th term of the sequence.

What is \(u_4\) of this sequence?

\(n\)	0	1	2	3	4	5	\(\dots\)
\(u_n\)	3	5	7	9	11	13	\(\dots\)

A sequence can be defined by:

• the first term (starting number), and
• a recursive rule that tells how to obtain each term from the previous one.

Write the sequence defined by: the first term is \(2\), and each term is obtained by adding \(3\) to the previous term.