Lists with an order
Sequences and terms
A list of numbers
Patterns are everywhere: in nature, art, music and money. The book looks at patterns made of numbers. Here are the square numbers: 1, 4, 9, 16, 25, 36, …
Swap the 4 and the 9: 1, 9, 4, 16, 25, 36, … Is that still the same list?
What this lesson covers
The idea
A sequence is an ordered list of numbers, each number being a term; a sequence may be finite or infinite, and three dots … show that it continues indefinitely.
A list of numbers
Patterns are everywhere: in nature, art, music and money. The book looks at patterns made of numbers. Here are the square numbers: 1, 4, 9, 16, 25, 36, …
Swap the 4 and the 9: 1, 9, 4, 16, 25, 36, … Is that still the same list?
- Yes, the numbers are the same
- No, the order has changed
Open the lists
Two lists are hidden. Open each one with Next term. Tap a card to see its place in the list.
Terms in order
A sequence is an ordered list of numbers. Each number is a term. A sequence may be finite (it stops) or infinite (the three dots … show that it continues indefinitely).
In 1, 4, 9, 16, 25, 36, … the first term is 1, the second is 4 and the fifth is 25. The order matters: that is why it is an *ordered* list.
Notes
A sequence is an ordered list of numbers; each number is a term. It may be finite or infinite, and three dots … show that it continues indefinitely.
Check yourself
In the sequence 1, 4, 9, 16, 25, 36, … which number is the fifth term?
Which of these is a finite sequence?
How many terms does the sequence 6, 12, 24, 48, 96 have?
Answer: 5
The terms are 6, 12, 24, 48 and 96. That is 5 terms.
What do the three dots … tell us at the end of 1, 3, 5, 7, 9, 11, …?
- 16. 16 is the fourth term. Count 1, 4, 9, 16, and then comes the fifth.
- 25 — correct. Yes. The terms in order are 1, 4, 9, 16, 25, so 25 is the fifth term.
- 36. 36 is the sixth term. The fifth comes just before it.
- 1, 2, 3, 4, 5, 6, …. The three dots say it continues indefinitely. This list of natural numbers never stops, so it is infinite.
- 6, 12, 24, 48, 96 — correct. Yes. There are no dots: the list stops after the fifth term, 96.
- 1, 3, 5, 7, 9, 11, …. The odd numbers go on and on, and the three dots show it. That is an infinite sequence.
- Three more terms are missing. The dots do not count terms. They say that the sequence never stops.
- The sequence stops after 11. If it stopped after 11 there would be no dots. The dots show it continues.
- The sequence continues indefinitely — correct. Yes. The dots mean the list goes on for ever, so the sequence is infinite.