Generating a sequence using a term-to-term rule
I can appreciate that a sequence can be generated and described using term-to-term approaches.
- Year 8
Generating a sequence using a term-to-term rule
I can appreciate that a sequence can be generated and described using term-to-term approaches.
Lesson details
Key learning points
- Sequences can be created using a rule that tells you how to find the next term from the current one.
- These sequences could be related additively or multiplicity.
- These sequences could be related in other ways.
- This term-to-term method is time-consuming when you want to find higher terms in the sequence.
- It is possible to describe the rule when given some of the terms although this may not be unique.
Keywords
Term-to-term - A term-to-term rule describes how to calculate the next term in the sequence from the previous term.
Common misconception
The difference in the given terms divided by the number of missing terms gives the common difference
Write the sequence out with gaps for the missing terms. Model how many additions (jumps) to get from one known term to the next.
Equipment
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Which of these best describes what a term in a sequence is?
Q2.What would be the next value in this sequence if it has a constant additive rule? -1, 6, , ...
Q3.What would be the next value in this sequence if it has a constant multiplicative rule? -1, 6, , ...
Q4.Match the next 2 numbers in the sequence which starts 16, 4, ... with the rule the sequence is following.
..., 1, 0.25, ... -Â Multiply the previous term by $$1\over 4$$
..., -8, -20, ... -Â add (-12) to the previous term
..., -2, -5, ... -Â halve the previous term and subtract 4
..., -6, -14, ... -Â subtract 12, then subtract 10, then subtract 8 ...
..., 2, 10, ... -Â subtract 12, then subtract 2, then subtract -8 ...
Q5.Calculate the number halfway between 16 and 34
Q6.Match these calculations to the correct answers.
$$4.1\times 0.1$$ -Â 0.41
$$4.1\div 0.1$$ -Â 41
$$41\times 10$$ -Â 410
$$41\times 0.1 $$ -Â 4.1
$$410\div 0.1$$ -Â 4100
Assessment exit quiz
6 Questions
Q1.Which of these best describes what a term-to-term rule is?
Q2.Match the term-to-term rules with the sequences
8, 12, 18, 27, ... -Â multiply the previous term by $$3\over 2$$
8, 12, 16, 20, ... -Â add 4 to the previous term
8, 12, 20, 32, ... -Â add 4, then add 8, then add 12, ...
8, 12, 20, 36, ... -Â double the previous term then subtract 4
8, 12, 17, 23, ... -Â add 4, then add 5, then add 6, ...
Q3.A sequence starts 7,10, ... What is the 10th term if the term to term rule is 'add 3 to the previous term'?
Q4.Which of the statements below is a limitation of using term-to-term rules?
Q5.What is the term-to-term rule for this sequence with a constant additive pattern? 17, ?, 29, ?, 41, ...
Q6.What is the term-to-term rule for the constant additive sequence with 2nd term = 63 and 7th term = 23?
