New
New
Year 11
Higher

Identifying values in an arithmetic sequence

I can identify through the n^th term whether a value appears in a given sequence.

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New
New
Year 11
Higher

Identifying values in an arithmetic sequence

I can identify through the n^th term whether a value appears in a given sequence.

Link copied to clipboard

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Lesson details

Key learning points

  1. The n^th term rule can identify what term number a given number is.
  2. If the term number is not a positive integer, then the term is not in the sequence.

Keywords

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

  • 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

As long as the equation can be solved, the value will be in the sequence.

For the value to be in the sequence, the value for n must be a positive integer. If it is not, then the value is not in the sequence as the term number must be a positive integer.


To help you plan your year 11 maths lesson on: Identifying values in an arithmetic sequence, download all teaching resources for free and adapt to suit your pupils' needs...

Pupils may not see why they need a different method to 'counting on'. Ask them to calculate the term value for a large term number such as 1987 to help them see why. The sequence could be made more tricky by having a negative common difference such as -17
Teacher tip

Licence

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).

Lesson video

6 Questions

Q1.
An arithmetic sequence has a common additive difference between successive terms. They are also frequently called __________ sequences.
Correct answer: linear
increasing
adding up
geometric
Q2.
In the linear equation y=6x3 what is the value of y when x=3?
Correct Answer: 15, y=15
Q3.
In the linear equation y=6x3 what is the value of x when y=3?
Correct Answer: 1, x=1
Q4.
Match the x values to their respective y values for the linear equation y=57x
Correct Answer:x=1,y=2

y=2

Correct Answer:x=2,y=9

y=9

Correct Answer:x=3,y=16

y=16

Correct Answer:x=4,y=23

y=23

Correct Answer:x=5,y=30

y=30

Correct Answer:x=10,y=65

y=65

Q5.
Solve the equation 3x17=451 x=
Correct Answer: 156, x=156
Q6.
Solve the equation 4x+81=1000 and give your answer as a decimal. x=
Correct Answer: 229.75, x=229.75

6 Questions

Q1.
In sequence notation, T is the term and n is the term's __________.
Correct answer: position in the sequence
value
additive difference
Q2.
Which of these are the first three terms of the sequence 2n1?
Correct answer: 1
2
Correct answer: 3
4
Correct answer: 5
Q3.
Which of these are the first five terms of the sequence 207n?
20,13,6,1,8,...
20,13,6,2,9,...
Correct answer: 13,6,1,8,15...
13,6,2,9,16...
Q4.
What is the 50th term of the sequence 8n38?
Correct Answer: 362
Q5.
What position is the term 258 in the sequence 8n38?
Correct Answer: 37, 37th, n=37
Q6.
Which of the below are in the sequence 12n15?
Correct answer: 285
290
Correct answer: 993
Correct answer: 1197
1200
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