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Year 9

Extending thinking about sequences

I can appreciate that abstract sequences can have negative values.

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New
New
Year 9

Extending thinking about sequences

I can appreciate that abstract sequences can have negative values.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. When you move away from physical representations of sequences, you can think abstractly.
  2. You can consider what happens if there was not a first term.
  3. The sequence could extend forward and backwards.
  4. You can generate previous terms using the inverse of the term-to-term rule.

Common misconception

All sequences can go on infinitely.

When we think abstractly and start a sequence such as 8, 10, 12, 14, 16, ... it is possible that it goes on infinitely. However, if we applied this sequence to a context such as pairs of pupils getting on a bus, then a physical limit will apply.

Keywords

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

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

Ask pupils to come up with their own examples of concrete sequences that we find in the real world and explain their physical limitations. Then ask them to think abstractly, and describe what would happen to the sequence if no physical limit existed.
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).

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Starter quiz

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6 Questions

Q1.
An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a __________.
Correct answer: constant
multiplier
negative number
positive number
variable
Q2.
Find the next term in the arithmetic sequence -25, -18, -11, -4, .
Correct Answer: 3
Q3.
Find the missing term in the arithmetic sequence 27, , 55, 69, 83, ...
Correct Answer: 41
Q4.
Find the common ratio of the geometric sequence 0.4, 1.6, 6.4, 25.6, ...
0.25
0.4
0.6
Correct answer: 4
6
Q5.
Find the next term in the geometric sequence 0.4, 1.6, 6.4, 25.6, , ... Give your answer as a decimal.
Correct Answer: 102.4
Q6.
Which statements are true of the sequence 1920, 960, 480, 240, 120, ... ?
It is a decreasing sequence therefore will contain negative values in the future
It is a geometric sequence with a common ratio greater than 1
Correct answer: It is a geometric sequence with a common ratio less than 1
It will eventually start to increase again.
Correct answer: It will never reach zero.

Exit quiz

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6 Questions

Q1.
In mathematics, sequences can be described as concrete or __________.
Correct answer: abstract
non-concrete
Q2.
In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. This is an example of __________ sequence.
Correct answer: a concrete
an abstract
Q3.
In 1980, the world marathon record was 2 hrs 10 mins. In the year 2000, it was 2 hrs 5 mins. In the year 2020, it was 2 hrs 0 mins. Why is this concrete sequence limited?
It is not limited. The pattern will continue at -5 minutes per decade.
Correct answer: Records are decreasing now but can never reach zero. There are physical limits.
The record of 2hrs 0 mins cannot be broken.
Q4.
What value would come before this geometric sequence? 196, 1372, 9604, 67 228, ...
Correct Answer: 28
Q5.
Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Using the sequence to predict the population for year 5.
An image in a quiz
3 074 173
3 407 173
Correct answer: 3 704 173
3 707 143
Q6.
Scientists begin to study the population of a particular fish in the North Sea and find it forms a geometric sequence. Estimate the population of the fish the year before the study began.
An image in a quiz
Correct Answer: 2300000, 2 300 000, 2,300,000