Starter quiz
- An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a __________.
- constant ✓
- multiplier
- negative number
- positive number
- variable
-
- Find the next term in the arithmetic sequence -25, -18, -11, -4,______.
- '3' ✓
- Find the missing term in the arithmetic sequence 27, ______, 55, 69, 83, ...
- '41' ✓
- Find the common ratio of the geometric sequence 0.4, 1.6, 6.4, 25.6, ...
- 0.25
- 0.4
- 0.6
- 4 ✓
- 6
-
- Find the next term in the geometric sequence 0.4, 1.6, 6.4, 25.6, ______, ... Give your answer as a decimal.
- '102.4' ✓
- 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
- It is a geometric sequence with a common ratio less than 1 ✓
- It will eventually start to increase again.
- It will never reach zero. ✓
-
Exit quiz
- In mathematics, sequences can be described as concrete or __________.
- abstract ✓
- non-concrete
-
- 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.
- a concrete ✓
- an abstract
-
- 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.
- Records are decreasing now but can never reach zero. There are physical limits. ✓
- The record of 2hrs 0 mins cannot be broken.
-
- What value would come before this geometric sequence? 196, 1372, 9604, 67 228, ...
- '28' ✓
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.- 3 074 173
- 3 407 173
- 3 704 173 ✓
- 3 707 143
-
- 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.
- '2300000' ✓
Worksheet
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Presentation
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Video
Lesson Details
Key learning points
- When you move away from physical representations of sequences, you can think abstractly.
- You can consider what happens if there was not a first term.
- The sequence could extend forward and backwards.
- 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.
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