Securing understanding of arithmetic sequences
I can begin to generalise a sequence.
Securing understanding of arithmetic sequences
I can begin to generalise a sequence.
Lesson details
Key learning points
- The n^th term is the generalised way of expressing any term in a sequence.
- For an arithmetic sequence, it will have the form d(n-1)+a
- The a refers to the first term of the sequence.
- The d refers to the common difference between any two consecutive terms.
Common misconception
Misinterpreting the values in an expression for the n^th term. For example, given the n^th term $$3n-5$$ pupils may think that this relates to a sequence that is decreasing by 5 each time
Remind students about how the expression for the n^th term relates to multiples of a number (times tables) and then a shift. For example, 4, 9, 14, 19, ... can be seen as the 5 times table shifted down 1.
Keywords
Arithmetic/ linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant
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).
Video
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Starter quiz
6 Questions
$$3n+2$$ -
$$5, 8, 11, 14, 17, ...$$
$$2n+3$$ -
$$5, 7, 9, 11, 13, ...$$
$$6n-1$$ -
$$5, 11, 17, 23, 29, ...$$
$$6-n$$ -
$$5, 4, 3, 2, 1, ...$$
$$5+n$$ -
$$6, 7, 8, 9, 10, ...$$
$$1-6n$$ -
$$-5, -11, -17, -23, -29, ...$$
Exit quiz
6 Questions
$$3n+9$$ -
$$12, 15, 18, 21, 24, ...$$
$$9n+3$$ -
$$12, 21, 30, 39, 48, ...$$
$$9n-3$$ -
$$6, 15, 24, 33, 42, ...$$
$$3n-9$$ -
$$-6,-3,0,3,6, ...$$
$$9-3n$$ -
$$6,3,0,-3,-6, ...$$