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.

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.

## 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.

### 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?"

### 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.

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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 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
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 - $$17-3a$$

## 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 .
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?
4
7
1
13
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: $$n \times 2 + 10$$