ANALYSING PATTERNS - 29/9/26 - AT3 REVISION

What is a sequence in mathematics?

A sequence is a list of numbers or objects in a specific order where the arrangement of the numbers matters.

What is the difference between a set and a sequence?

A set is a group of numbers where order does not matter, and duplicates are not included, while a sequence is an ordered list where the arrangement and occurrences of numbers matter.

What does finite mean in terms of sequences?

A finite sequence has a specific number of elements.

What does infinite mean in terms of sequences?

An infinite sequence has no end; it continues indefinitely.

Give an example of a repeating sequence.

{0,1,0,1,0,1} is an example of a repeating sequence.

Give an example of a non-repeating sequence.

{1,2,3,4,5,6} is an example of a non-repeating sequence.

What are arithmetic sequences?

Arithmetic sequences are sequences where each term is generated by adding a constant difference to the previous term.

What are geometric sequences?

Geometric sequences are sequences where each term is generated by multiplying the previous term by a constant ratio.

How to identify the rule of a sequence based on addition?

Check for a common difference between consecutive terms.

How to identify the rule of a sequence based on multiplication?

Check for a common ratio by dividing consecutive terms.

What is a common ratio?

A common ratio is the factor by which consecutive terms of a geometric sequence are multiplied.

Provide an example of a sequence created by skipping numbers.

{1,3,5,7,9,11,13…} is an example of a sequence created by skipping every second number.

What would the sequence be if the rule was subtracting by 5 starting from 50?

The sequence would be {50, 45, 40, 35, 30…}.

What can addition, subtraction, multiplication, and division create in sequences?

They can create rules that define how the sequence progresses.

State an example of how to identify a common difference in the sequence {0,4,8,12,16}.

Calculate the difference between consecutive terms, which is 4.

For the sequence {2,6,18,54}, what indicates it does not have a common difference?

The differences between terms are not consistent (4, 12, 36).

How do you find a common ratio?

Divide one term by its preceding term in the sequence.

What does the sequence {1,2,4,8,16} represent?

It represents a geometric sequence where each term is multiplied by 2.