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Year 8

Expressing an arithmetic sequence

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

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New
New
Year 8

Expressing an arithmetic sequence

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

Download all resources
Share activities with pupils

These resources will be removed by end of Summer Term 2025.

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Lesson details

Key learning points

  1. The general term of a sequence is called the n^th term.
  2. The value of n tells you what position in the sequence the term has.
  3. The term number tells you the value of n.

Keywords

  • N^th term - The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.

Common misconception

That $$n$$ is a term in the sequence. That $$n=10$$ means 10 is in the sequence.

Reiterate that $$n$$ is the term number. "$$n=10$$ means the 10th term. What is the 10th term number?"


To help you plan your year 8 maths lesson on: Expressing an arithmetic sequence, download all teaching resources for free and adapt to suit your pupils' needs...

Ask questions like "In this sequence, 7, 14, 21, 28, 35 what term number is 28? What is the $$n$$ value for the term 28?"
Teacher tip

Licence

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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Prior knowledge starter quiz

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6 Questions

Q1.
In sequences, a position-to-term rule describes what?
Correct answer: How to generate the term from the term number
How many terms there are in a sequence
How many positions there are in a sequence
Q2.
Multiplying $$x$$ by 4 and subtracting 7 is most simply written as which expression?
$$x \times 4 - 7$$
$$x \times -7 + 4$$
$$4 + x - 7$$
Correct answer: $$4x - 7$$
Q3.
Which position-to-term rule satisfies this sequence?
An image in a quiz
Add 3 each time.
Starts at 1 and counts up in 3.
Multiply by 3 and add 1
Correct answer: Multiply by 3 and subtract 2
Q4.
Which position-to-term rule links the pattern number to the number of squares?
An image in a quiz
Multiply the pattern number by 4.
Correct answer: Multiply the pattern number by 3 then add 1.
Add 3 to the pattern number.
Multiply the pattern number by 3 then subtract 1.
Q5.
For the arithmetic sequence starting 1, 4, 7, 10, 13, ... the position-to-term rule is 'multiply by 3 and subtract 2'. What therefore, is the 100$$^\text{th}$$ term?
300
302
Correct answer: 298
98
Q6.
Substitute the value $$a=6$$ into the below expressions. Order the value of the expressions from highest to lowest.
1 - $$3a-7$$
2 - $$2a-3$$
3 - $$7-a$$
4 - $$17-3a$$

Assessment exit quiz

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6 Questions

Q1.
The $$n^\text{th}$$ term of a sequence is the position of a term in a sequence where $$n$$ stands for the term .
Correct Answer: number, term number
Q2.
In sequences $$n=20$$ means what?
20 is in our sequence.
The sequence goes up 20 each term.
Correct answer: The 20$$^\text{th}$$ term number.
The sequence is our 20 times table.
Q3.
In this sequence when $$n=4$$ what is the term value?
An image in a quiz
4
Correct answer: 10
7
1
13
Q4.
In this sequence when $$T=4$$ what is the term number?
An image in a quiz
$$n=4$$
Correct answer: $$n=2$$
$$n=5$$
$$T=2$$
$$T=5$$
Q5.
What general rule links pattern number ($$n$$) to number of squares ($$T$$) in this case?
An image in a quiz
Correct answer: $$T = n \times 4 + 3$$
$$T = n + 4$$
$$T = n \times 4 - 1$$
$$T = n + 3$$
Q6.
What general rule links pattern number ($$n$$) to the perimeter of each shape?
An image in a quiz
$$+2$$
$$n + 2$$
$$12, 14, 16,\;$$...
$$n \times 4$$
Correct answer: $$n \times 2 + 10$$