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Year 9

Extrapolating a sequence

I can appreciate that there are other number sequences and the limitations of only seeing a few terms of a sequence.

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New
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Year 9

Extrapolating a sequence

I can appreciate that there are other number sequences and the limitations of only seeing a few terms of a sequence.

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Share activities with pupils
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Lesson details

Key learning points

  1. There are more sequences than the ones seen so far.
  2. A numerical sequence is just a set of numbers often following a rule.
  3. If you only see a few of the terms, it is possible to incorrectly deduce the rule.

Keywords

  • Arithmetic/linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant.

  • Geometric sequence - A geometric sequence is a sequence with a constant multiplicative relationship between successive terms.

Common misconception

Sequences are either arithmetic or geometric.

There are many ways sequences can be generated and you can usually find more than one rule than can fit the first few terms of a sequence. Exploring these will ensure pupils don't have a narrow experience of sequences.

Pupils can come up with ways to generate a sequence that they think might look like they fit one rule when they have used a different rule.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
Which of these are triangular numbers?
Correct answer: 1
8
12
Correct answer: 15
Correct answer: 21
Q2.
Which of these are prime numbers?
1
Correct answer: 2
Correct answer: 11
Correct answer: 13
15
Q3.
7, 8, 15, 23, 38 ... are the first five terms of a sequence. Which of these could be a rule for the sequence?
Add 1, add 3, add 5 and so on, differences increasing by 2 each time.
Add 1, add 7, add 13 and so on, differences increasing by 6 each time.
Correct answer: Add the two previous terms to get the next term.
Multiply the two previous terms to get the next term.
Multiply the previous term by 2 and subtract 1 to get the next term.
Q4.
A linear sequence starts -4, 6, ... . The next term is .
Correct Answer: 16
Q5.
A geometric sequence starts -4, 6, ... . What is the next term?
$$-12$$
Correct answer: $$-9$$
$$4$$
$$9$$
$$12$$
Q6.
Which of these could be the first 5 terms in a sequence with a common second difference?
27, 64, 125, 216, 343, ...
Correct answer: 28, 36, 45, 55, 66, ...
30, 52, 76, 98, 122, ...
32, 48, 72, 108, 162, ...
Correct answer: 36, 49, 64, 81, 100, ...

Exit quiz

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6 Questions

Q1.
Which of these could be a rule for generating the sequence 8, 16, 32, ...?
Correct answer: Multiply the previous term by 2 to get the next term.
Add 8 to the previous term to get the next term.
Correct answer: Add 8, then add 16 then add 24; common second difference of 8.
Add the two prevous terms to get the next term.
Q2.
Izzy says the next term in the sequence 1, 3, 6, 10, ... must be 15. Why is she incorrect?
These are a triangular numbers, they are not a sequence.
There is not a common difference of 5 between successive terms.
Correct answer: The pattern may change after the fourth term.
Sequences must have a constant additive or multiplicative rule.
Q3.
Which of these could be a rule for the sequence: 37, 41, 43, 47, 53, ...?
Correct answer: Prime numbers over 30 written in ascending order
A sequence which alternates between adding 4 and adding 2
A linear sequence with common difference +4
Sequence of numbers one more than the square numbers
Integers where the digits sum to multiples of 5
Q4.
Which of these could be the rule for the sequence starting 17, 19, 20, ...?
Odd numbers greater than 15.
Correct answer: Add 2, add 1, add 0, add -1; common second difference of -1.
Correct answer: Integers greater than 16 where the digits sum to even numbers.
Numbers with nine letters when written in English.
Add the two previous numbers and subtract 10 to get the next number.
Q5.
Which of these could be the rule for the sequence starting 6, 7, 9, ...?
Linear sequence with a common difference of +2
Correct answer: Sequence which adds 1, then 2, then 3; common second difference of 1
Correct answer: Double the previous term then subtract 5 to get the next term
Correct answer: Number of letters in the English words for days of the week, starting on Monday
Number of letters in the English words for the months starting on August
Q6.
Match each sequence which start with the terms 3, 6, ... to the correct rule.
Correct Answer:3, 6, 9, 12, ...,add 3 to the previous term to get the next term.

add 3 to the previous term to get the next term.

Correct Answer:3, 6, 12, 24, ...,multiply the previous term by 2 to get the next term.

multiply the previous term by 2 to get the next term.

Correct Answer:3, 6, 10, 15, ...,triangular numbers greater than 1.

triangular numbers greater than 1.

Correct Answer:3, 6, 12, 21, ...,add 3, add 6, add 9, common second difference of 3.

add 3, add 6, add 9, common second difference of 3.

Correct Answer:3, 6, 15, 42, ...,triple the previous term and subtract 3 to get the next term.

triple the previous term and subtract 3 to get the next term.