New

New

Year 8

# Calculating any term

I can calculate any term using the n^th term.

New

New

Year 8

# Calculating any term

I can calculate any term using the n^th term.

## Lesson details

### Key learning points

- The position to term rule can be expressed using n.
- A sequence can be generated using successive values of n .
- Any term can be calculated using the n^th term.

### Common misconception

That the sequence $$3n+2$$ starts with 3 and adds 2, or starts with 2 and adds 3.

Calculate the first few terms. Ask, "When $$n = 1$$ what is the term value?" This is the first value for our sequence.

### Keywords

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

Discuss the misconceptions very openly. Ask questions like, "What does the sequence $$8n+23$$ begin with? Is it 8? 23? 31?". Address why it is 31. This will also help future learning on finding $$n$$^th terms.

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).

## Video

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## Starter quiz

Download starter quiz

### 6 Questions

Q1.

Which of these words is also used to describe an arithmetic sequence?

Positive.

Quadratic.

Correct answer: Linear.

Linear.

Geometric.

Q2.

Which is the simplified version of $$2 \times a + 5 \times b + 3$$?

Correct answer: $$2a+5b+3$$

$$2a+5b+3$$

$$7ab+3$$

$$10ab$$

It is already in it's simplest form.

Q3.

If $$a=5$$ and $$b=7$$ what is the value of the expression $$2a+5b+3$$?

25 + 57 + 3

85

42

Correct answer: 48

48

Q4.

When $$n=5$$ what is the term value?

$$T=5$$

$$n=2$$

2

Correct answer: $$T=11$$

$$T=11$$

+2

Q5.

Evaluate the expression $$70-3x$$ when $$x=50$$.

Correct answer: -80

-80

20

-30

-50

220

Q6.

Given that $$a=9$$. $$b=-7$$. Put these expressions in order from lowest to highest value.

1 - $$3b-5a$$

1

- $$3b-5a$$

2 - $$5(a+3b)$$

2

- $$5(a+3b)$$

3 - $$-5a-3b$$

3

- $$-5a-3b$$

4 - $$5a+3b$$

4

- $$5a+3b$$

5 - $$5a-3b$$

5

- $$5a-3b$$

## Exit quiz

Download exit quiz

### 6 Questions

Q1.

The $$n^\text{th}$$ term can be used to calculate any term in a sequence so we can call it a __________ for finding the $$n^\text{th}$$ term.

equation

Correct answer: formula

formula

sequence

term value

Q2.

If the $$n^\text{th}$$ term is $$3n+7$$ what are the first five terms?

3, 10, 17, 24, 31, ...

7, 10, 13, 16, 19, ...

10, 17, 24, 31, 38, ...

Correct answer: 10, 13, 16, 19, 22, ...

10, 13, 16, 19, 22, ...

Q3.

What is the 5$$^\text{th}$$ term of $$0.3n + 0.07$$?

0.37

Correct answer: 1.57

1.57

2.2

1.75

5.37

Q4.

What are the first five terms of $$10-2n$$?

10, 8, 6, 4, 2, ...

12, 10, 8, 6, 4, ...

Correct answer: 8, 6, 4, 2, 0, ...

8, 6, 4, 2, 0, ...

-2, -4, -6, -8, -10 ...

Q5.

Order these term values from lowest to highest.

1 - The 50$$^\text{th}$$ term of the sequence $$2n-1$$.

1

- The 50$$^\text{th}$$ term of the sequence $$2n-1$$.

2 - The 15$$^\text{th}$$ term of the sequence $$6n+10$$.

2

- The 15$$^\text{th}$$ term of the sequence $$6n+10$$.

3 - The 101$$^\text{st}$$ term of the sequence $${1 \over 2} n + 50$$.

3

- The 101$$^\text{st}$$ term of the sequence $${1 \over 2} n + 50$$.

4 - The 9$$^\text{th}$$ term of the sequence $$200-11n$$.

4

- The 9$$^\text{th}$$ term of the sequence $$200-11n$$.

Q6.

Which statements are true for the arithmetic sequence $$1.25n-0.3$$?

The sequence contains the number 1.25

Correct answer: The sequence contains the number 2.2

The sequence contains the number 2.2

The sequence goes down by 0.3 each time.

Correct answer: The sequence goes up by 1.25 each time.

The sequence goes up by 1.25 each time.

Correct answer: The sequence starts at 1.25-0.3

The sequence starts at 1.25-0.3