- Year 9
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.
Keywords
Arithmetic/ linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is constant
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.
Licence
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.The arithmetic (linear) sequence 17, 21, 25, 29, 33, ... has a(n) _________ of +4.
Q2.Which of these sequences are arithmetic?
Q3.Match the $$n^{\text{th}}$$ term to the first five terms of each sequence.
$$3n+2$$ -Â $$5, 8, 11, 14, 17, ...$$
$$2n+3$$ -Â $$5, 7, 9, 11, 13, ...$$
$$6n-1$$ -Â $$5, 11, 17, 23, 29, ...$$
$$6-n$$ -Â $$5, 4, 3, 2, 1, ...$$
$$5+n$$ -Â $$6, 7, 8, 9, 10, ...$$
$$1-6n$$ -Â $$-5, -11, -17, -23, -29, ...$$
Q4.The solution to the two-step equation $$8x-13=83$$ is $$x=$$
Q5.Which is true of the solution to the equation $$3x-10=3$$
Q6.$$8, 13, 18, 23, 28, ...$$ are the first five terms of which sequence?
Assessment exit quiz
6 Questions
Q1.In the $$n^{\text{th}}$$ term expression $$9n-7$$, you call $$9$$ the __________ of $$n$$.
Q2.What is the common difference in the arithmetic sequence $$6n-3$$?
Q3.Match each sequence to its $$n^{\text{th}}$$ term.
$$3n+9$$ -Â $$12, 15, 18, 21, 24, ...$$
$$9n+3$$ -Â $$12, 21, 30, 39, 48, ...$$
$$9n-3$$ -Â $$6, 15, 24, 33, 42, ...$$
$$3n-9$$ -Â $$-6,-3,0,3,6, ...$$
$$9-3n$$ -Â $$6,3,0,-3,-6, ...$$
Q4.405 is a term in the arithmetic sequence with the rule $$7n-50$$. What is its position in the sequence? $$n=$$
Q5.Is $$189$$ a term in the arithmetic sequence $$7n-50$$?
Q6.Which expressions could be used to generalise the arithmetic sequence 5, 9, 13, 17, 21, ...?
