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Year 9

Securing understanding of arithmetic sequences

I can begin to generalise a sequence.

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New
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Year 9

Securing understanding of arithmetic sequences

I can begin to generalise a sequence.

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Share activities with pupils
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These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. The n^th term is the generalised way of expressing any term in a sequence.
  2. For an arithmetic sequence, it will have the form d(n-1)+a
  3. The a refers to the first term of the sequence.
  4. 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.


To help you plan your year 9 maths lesson on: Securing understanding of arithmetic sequences, download all teaching resources for free and adapt to suit your pupils' needs...

This lesson is an opportunity to review and build fluency with finding and using the n^th term of arithmetic sequences and for students who are confident they will enjoy exploring a different way to think about the n^th term through $$d(n-1)+a$$
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This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Lesson video

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Starter quiz

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6 Questions

Q1.
The arithmetic (linear) sequence 17, 21, 25, 29, 33, ... has a(n) _________ of +4.
$$n^{\text{th}}$$ term
$$1^{\text{st}}$$ term
Correct answer: common difference
multiplier
Q2.
Which of these sequences are arithmetic?
Correct answer: 2, 6, 10, 14, ...
Correct answer: 2, 7, 12, 17, ...
2, 8, 15, 23, ...
2, 4, 8, 16, ...
Correct answer: 2, -1, -4, -7, ...
Q3.
Match the $$n^{\text{th}}$$ term to the first five terms of each sequence.
Correct Answer:$$3n+2$$,$$5, 8, 11, 14, 17, ...$$
tick

$$5, 8, 11, 14, 17, ...$$

Correct Answer:$$2n+3$$,$$5, 7, 9, 11, 13, ...$$
tick

$$5, 7, 9, 11, 13, ...$$

Correct Answer:$$6n-1$$,$$5, 11, 17, 23, 29, ...$$
tick

$$5, 11, 17, 23, 29, ...$$

Correct Answer:$$6-n$$,$$5, 4, 3, 2, 1, ...$$
tick

$$5, 4, 3, 2, 1, ...$$

Correct Answer:$$5+n$$,$$6, 7, 8, 9, 10, ...$$
tick

$$6, 7, 8, 9, 10, ...$$

Correct Answer:$$1-6n$$,$$-5, -11, -17, -23, -29, ...$$
tick

$$-5, -11, -17, -23, -29, ...$$

Q4.
The solution to the two-step equation $$8x-13=83$$ is $$x=$$
Correct Answer: 12, x=12, twelve
Q5.
Which is true of the solution to the equation $$3x-10=3$$
It is a positive integer.
It is a negative integer.
Correct answer: It is non-integer.
It has no solution.
Q6.
$$8, 13, 18, 23, 28, ...$$ are the first five terms of which sequence?
$$8n+5$$
$$5n+8$$
Correct answer: $$5n+3$$
$$5n-3$$

Exit quiz

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6 Questions

Q1.
In the $$n^{\text{th}}$$ term expression $$9n-7$$, you call $$9$$ the __________ of $$n$$.
$$1^{st}$$ term
Correct answer: coefficient
equation
expression
Q2.
What is the common difference in the arithmetic sequence $$6n-3$$?
-6
-3
3
Correct answer: 6
Q3.
Match each sequence to its $$n^{\text{th}}$$ term.
Correct Answer:$$3n+9$$,$$12, 15, 18, 21, 24, ...$$
tick

$$12, 15, 18, 21, 24, ...$$

Correct Answer:$$9n+3$$,$$12, 21, 30, 39, 48, ...$$
tick

$$12, 21, 30, 39, 48, ...$$

Correct Answer:$$9n-3$$,$$6, 15, 24, 33, 42, ...$$
tick

$$6, 15, 24, 33, 42, ...$$

Correct Answer:$$3n-9$$,$$-6,-3,0,3,6, ...$$
tick

$$-6,-3,0,3,6, ...$$

Correct Answer:$$9-3n$$,$$6,3,0,-3,-6, ...$$
tick

$$6,3,0,-3,-6, ...$$

Q4.
405 is a term in the arithmetic sequence with the rule $$7n-50$$. What is its position in the sequence? $$n=$$
Correct Answer: 65, sixty-five, n=65, 65th
Q5.
Is $$189$$ a term in the arithmetic sequence $$7n-50$$?
Yes, because $$189$$ is odd and the sequence contains a lot of odd numbers.
Yes, because $$189\div7=27$$
No, because $$189$$ is odd and the sequence is mostly even.
Correct answer: No, because $$7n-50=189$$ has a non-integer solution.
Q6.
Which expressions could be used to generalise the arithmetic sequence 5, 9, 13, 17, 21, ...?
$$5n+4$$
Correct answer: $$4n+1$$
$$5+4n$$
Correct answer: $$5+4(n-1)$$
$$4+5(n-1)$$