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

1. A graph can be used to identify if a particular number is a term in a sequence.
2. The nth term rule can be used to determine if a number is in the sequence .
3. 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).

## Starter quiz

### 6 Questions

Q1.
The calculation 6(20) - 8 would find the 20$$^\text{th}$$ of the sequence $$6n-8$$.
Q2.
Which of these describe features of the sequence $$5n-9$$?
Correct answer: 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
Correct answer: 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 - 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 decreasing pattern of values.
You get a curve.
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
Q6.
Put these term values in order of size. Start with the smallest.
1 - The 80$$^\text{th}$$ term of the sequence $$6n-35$$
2 - The 50$$^\text{th}$$ term of the sequence $$596-3n$$
3 - The 60$$^\text{th}$$ term of the sequence $$9n-88$$
4 - The 95$$^\text{th}$$ term of the sequence $$5n-11$$
5 - The 50$$^\text{th}$$ term of the sequence $$9n+19$$

## Exit quiz

### 6 Questions

Q1.
The sequence 37, 47, 57, 67, 77, ... could be described as which?
Non-linear
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.
Correct answer: 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 $$5n+13$$?
103
1001
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 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: $$n=50$$
$$n=100$$
$$n=300$$
$$n=600$$
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 the 112.25$$^\text{th}$$ term.
Correct answer: 881 is not a term because 112.25 is not a whole number.