Number Sequences – Comprehensive Explanations and Clear Examples

In $\textit{sequences}$, it is important that we can;

A $\textit{number sequence}$ is an ordered list of numbers defined by a rule.

The numbers in the sequence are said to be its $\textit{terms}$.

A sequence that continues forever is called an $\textit{infinite sequence}$.

A sequence that terminates is called a $\textit{finite sequence}$.

Write down the first four terms of the sequence if you start with $5$ and add $3$ each time.

$ 5, 8, 11, 14 $

Write down the first four terms of the sequence if you start with $99$ and subtract $4$ each time.

$ 99, 95, 91, 87 $

Write down the first four terms of the sequence if you start with $4$ and multiply $3$ each time.

$ 4, 12, 36, 108 $

Describe the sequence: $ 3, 7, 11, 14, \cdots $.

The sequence starts at $ 3 $, and each term is $ 4 $ more than the previous term.

Describe the sequence: $76, 73, 70, 67, \cdots$.

The sequence starts at $76$, and each term is $3$ less than the previous term.

Describe the sequence: $ 2, 6, 18, 54, \cdots $.

The sequence starts at $ 2 $; each term is $ 3 $$ times the previous term.

Describe the sequence: $1, 4, 9, 16, \cdots$.

$ 1^2=1,2^2=4,3^2=9,4^2=16 $
Each term is the square of the term number.

Find the next two terms of $ 1, 8, 27, 64 $.

Each term is the cube of the term number.
$ \begin{align}5^3 &= 125 \\ 6^3 &= 216 \end{align} $

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