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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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Lesson 7 of 12

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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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Key learning points

The general term of a sequence is called the n^th term.
The value of n tells you what position in the sequence the term has.
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?"

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?"

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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).

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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?

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?

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

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?

Correct answer: 10

Q4.
In this sequence when $$T=4$$ what is the term number?

$$n=4$$

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?

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?

$$+2$$

$$n + 2$$

$$12, 14, 16,\;$$...

$$n \times 4$$

Correct answer: $$n \times 2 + 10$$

Lesson appears in

UnitMaths / Sequences

Maths

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Expressing an arithmetic sequence

Expressing an arithmetic sequence

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.In sequences, a position-to-term rule describes what?

Q2.Multiplying $$x$$ by 4 and subtracting 7 is most simply written as which expression?

Q3.Which position-to-term rule satisfies this sequence?

Q4.Which position-to-term rule links the pattern number to the number of squares?

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?

Q6.Substitute the value $$a=6$$ into the below expressions. Order the value of the expressions from highest to lowest.

Assessment exit quiz

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 .

Q2.In sequences $$n=20$$ means what?

Q3.In this sequence when $$n=4$$ what is the term value?

Q4.In this sequence when $$T=4$$ what is the term number?

Q5.What general rule links pattern number ($$n$$) to number of squares ($$T$$) in this case?

Q6.What general rule links pattern number ($$n$$) to the perimeter of each shape?

Lesson appears in

UnitMaths / Sequences

Maths

Q1.
In sequences, a position-to-term rule describes what?

Q2.
Multiplying $$x$$ by 4 and subtracting 7 is most simply written as which expression?

Q3.
Which position-to-term rule satisfies this sequence?

Q4.
Which position-to-term rule links the pattern number to the number of squares?

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?

Q6.
Substitute the value $$a=6$$ into the below expressions. Order the value of the expressions from highest to lowest.

Q1.
The $$n^\text{th}$$ term of a sequence is the position of a term in a sequence where $$n$$ stands for the term .

Q2.
In sequences $$n=20$$ means what?

Q3.
In this sequence when $$n=4$$ what is the term value?

Q4.
In this sequence when $$T=4$$ what is the term number?

Q5.
What general rule links pattern number ($$n$$) to number of squares ($$T$$) in this case?

Q6.
What general rule links pattern number ($$n$$) to the perimeter of each shape?