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Year 9

Checking understanding of arithmetic sequences

I can appreciate that any term in an arithmetic sequence can be expressed in terms of its position in the sequence and generate any term.

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New
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Year 9

Checking understanding of arithmetic sequences

I can appreciate that any term in an arithmetic sequence can be expressed in terms of its position in the sequence and generate any term.

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Lesson details

Key learning points

  1. An arithmetic sequence can be identified through a common difference between consecutive terms.
  2. Arithmetic sequences can be represented visually as well as algebraically.
  3. The formula for the n^th term allows us to generate any term in the sequence based on its position.

Keywords

  • Arithmetic/linear sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant

Common misconception

Pupils assume a sequence is arithmetic and only check the first few terms.

Encourage pupils to check all the terms of a sequence they are given to check that the pattern they think they have spotted is continuing.

Encourage pupils to represent sequences in a variety of ways (using numbers, diagrams, counters and graphically). Finding different, but correct ways to describe sequences and realising these simplify to the same thing will support pupils with the learning in this unit.
Teacher tip

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).

Lesson video

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Starter quiz

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6 Questions

Q1.
In the context of the arithmetic sequence 13, 20, 27, 34, 41, ..., you can call +7 the __________.
addition
$$n^{th}$$ term
sum
Correct answer: term-to-term rule
Q2.
Match each arithmetic (linear) sequence to its term-to-term rule.
Correct Answer:1, 5, 9, 13, 17, ...,+4

+4

Correct Answer:-4, -1, 2, 5, 8, ...,+3

+3

Correct Answer:2, -1, -4, -7, -10, ...,-3

-3

Correct Answer:3, -4, -11, -18, -25, ...,-7

-7

Correct Answer:3, 5, 7, 9, 11, ...,+2

+2

Correct Answer:-32, -25, -18, -11, -4, ...,+7

+7

Q3.
Select the terms that are in this arithmetic sequence: 7, 15, 23, 31, ...
$$89$$
Correct answer: $$87$$
$$80$$
Correct answer: $$55$$
$$50$$
Q4.
Which of these terms are in the sequence described by "Start on 5 and add 3 each time"?
3
Correct answer: 5
Correct answer: 8
15
Correct answer: 20
Q5.
Select the expressions that have a value of 33 when $$n=10$$.
Correct answer: $$4n-7$$
$$33+n$$
Correct answer: $$3n+3$$
$$33n$$
Correct answer: $$63-3n$$
Q6.
Find the value of the expression $$9-6n$$ when $$n=4$$.
-55
-24
Correct answer: -15
3
4

Exit quiz

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6 Questions

Q1.
An $$n^{\text{th}}$$ term expression such as $$7n-15$$ is called a ...
Correct answer: position-to-term rule
subtracting sequence
term-to-term rule
term-to-position rule
Q2.
Which of the below are arithmetic sequences?
Correct answer: 5, 10, 15, 20, 25, ...
5, 10, 20, 40, ...
Correct answer: 5, -5, -15, -25, ...
5, 11, 18, 26, 35, ...
Correct answer: 5, 12, 19, 26, 33, ...
Q3.
Match the $$n^{\text{th}}$$ term expression to the first term of the sequence.
Correct Answer:$$6n+3$$,$$9$$

$$9$$

Correct Answer:$$9n-5$$,$$4$$

$$4$$

Correct Answer:$$4n+1$$,$$5$$

$$5$$

Correct Answer:$$5n-3$$,$$2$$

$$2$$

Correct Answer:$$2n-5$$,$$-3$$

$$-3$$

Correct Answer:$$9-3n$$,$$6$$

$$6$$

Q4.
Which of the following are in the first five terms of the sequence $$5n-4$$?
-4
Correct answer: 1
5
9
Correct answer: 16
Q5.
Match each $$n^{\text{th}}$$ term expression to the $$50^{\text{th}}$$ term of the sequence. You may use a calculator.
Correct Answer:$$2n-17$$,$$83$$

$$83$$

Correct Answer:$$1.5n+7$$,$$82$$

$$82$$

Correct Answer:$$0.6n+50$$,$$80$$

$$80$$

Correct Answer:$$200-2.3n$$,$$85$$

$$85$$

Correct Answer:$$234-3n$$,$$84$$

$$84$$

Q6.
Which of these arithmetic sequences could be represented by this graph?
An image in a quiz
3, 8, 13, 18, 23, ...
-3, -8, -13, -18, -23, ...
-13, -8, -3, 2, 7, ...
8, 3, -2, -7, -12, ...
Correct answer: 13, 8, 3, -2, -7, ...