New

New

Year 8

# Justifying terms of a sequence

I can determine whether a number is a term of a given arithmetic sequence.

New

New

Year 8

# Justifying terms of a sequence

I can determine whether a number is a term of a given arithmetic sequence.

## Lesson details

### Key learning points

- A graph can be used to identify if a particular number is a term in a sequence.
- The nth term rule can be used to determine if a number is in the sequence .
- It is important to justify if a number is or is not a term in a sequence.

### Common misconception

It is impossible to tell if 174 368 is in the sequence -8,-3,2,7, ...

Generalising the rule for forming a given sequence can help us see if a value is in the sequence.

### Keywords

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

Graphical software can be used effective here to explore whether a given value is a term in a sequence.

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

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### 6 Questions

Q1.

The calculation 6(20) - 8 would find the 20$$^\text{th}$$ of the sequence $$6n-8$$.

Correct Answer: term

term

Q2.

Which of these describe features of the sequence $$5n-9$$?

Correct answer: It has a constant difference of +5

It has a constant difference of +5

It decreases by 9 each time

The terms always end in the digits 1 or 6

Correct answer: The positive terms always end in the digits 1 or 6

The positive terms always end in the digits 1 or 6

Correct answer: It starts at -4

It starts at -4

Q3.

What is the 75$$^\text{th}$$ term of the sequence $$6n-17$$?

675 - 17 = 658

6 + (75) - 17=64

Correct answer: 6(75) - 17 = 450 - 17 = 433

6(75) - 17 = 450 - 17 = 433

(6 - 17)75 = -11 $$\times$$ 75 = -825

Q4.

What happens when you plot an arithmetic sequence?

Correct answer: You get a straight line of values.

You get a straight line of values.

You get a decreasing pattern of values.

You get a curve.

Correct answer: You might see points in two quadrants.

You might see points in two quadrants.

You might plot points in all four quadrants.

Q5.

Calculate the 200$$^\text{th}$$ term of $$17.96-0.32n$$. You may use a calculator.

81.96

3528

-81.96

Correct answer: -46.04

-46.04

Q6.

Put these term values in order of size. Start with the smallest.

1 - The 80$$^\text{th}$$ term of the sequence $$6n-35$$

1

- The 80$$^\text{th}$$ term of the sequence $$6n-35$$

2 - The 50$$^\text{th}$$ term of the sequence $$596-3n$$

2

- The 50$$^\text{th}$$ term of the sequence $$596-3n$$

3 - The 60$$^\text{th}$$ term of the sequence $$9n-88$$

3

- The 60$$^\text{th}$$ term of the sequence $$9n-88$$

4 - The 95$$^\text{th}$$ term of the sequence $$5n-11$$

4

- The 95$$^\text{th}$$ term of the sequence $$5n-11$$

5 - The 50$$^\text{th}$$ term of the sequence $$9n+19$$

5

- The 50$$^\text{th}$$ term of the sequence $$9n+19$$

## Exit quiz

Download exit quiz

### 6 Questions

Q1.

The sequence 37, 47, 57, 67, 77, ... could be described as which?

Correct answer: Linear

Linear

Non-linear

Correct answer: Arithmetic

Arithmetic

Correct answer: Increasing

Increasing

Decreasing

Q2.

Which of the below statements supports the justification that 6941 is not in the arithmetic sequence starting 14, 19, 24, 29, 34, ...?

It's too large a number.

Correct answer: 14, 19, 24, 29, 34, ... is a translation of a $$5n$$ sequence.

14, 19, 24, 29, 34, ... is a translation of a $$5n$$ sequence.

Correct answer: The sequence will always end in the digit 4 or 9 in the ones position.

The sequence will always end in the digit 4 or 9 in the ones position.

6941 is an odd number, and the sequence begins with an even number.

Q3.

Which of the below will be common terms in the sequences $$2n+24$$ and $$5n+13$$?

Correct answer: 13 048

13 048

103

Correct answer: 888

888

1001

Correct answer: 8008

8008

Q4.

The first 8 terms of a sequence are plotted. Which term is incorrect in the plotting of this arithmetic sequence?

The 2$$^\text{nd}$$ term

The 4$$^\text{th}$$ term

Correct answer: The 6$$^\text{th}$$ term

The 6$$^\text{th}$$ term

The 8$$^\text{th}$$ term

Q5.

Which of the below is a useful estimation to start with when trying to find 315 in the sequence $$6n-9$$?

$$n=25$$

Correct answer: $$n=50$$

$$n=50$$

$$n=100$$

$$n=300$$

$$n=600$$

Q6.

What does this calculator display tell us?

881 is in the sequence $$8n-17$$

Correct answer: 881 is not in the sequence $$8n-17$$

881 is not in the sequence $$8n-17$$

881 is the 112.25$$^\text{th}$$ term.

Correct answer: 881 is not a term because 112.25 is not a whole number.

881 is not a term because 112.25 is not a whole number.