New
New
Year 11
Higher

Checking and securing rules for generating arithmetic sequences

I can identify the term-to-term rule and the position-to-term rule and express the latter algebraically.

New
New
Year 11
Higher

Checking and securing rules for generating arithmetic sequences

I can identify the term-to-term rule and the position-to-term rule and express the latter algebraically.

Lesson details

Key learning points

  1. The term-to-term rule is the common difference.
  2. Finding the common difference can help when finding the n^th term rule.
  3. Comparing the sequence to an appropriate multiplication table can help identify the translation that has been made.
  4. The n^th term can be found for all arithmetic sequences.

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

Arithmetic sequences only have a positive integer as the common difference.

Arithmetic sequences can be increasing or decreasing and can have any value for the common difference.

Challenge pupils to create their own arithmetic sequence that has a common difference that no one else will have chosen. This could lead to an arithmetic sequence with a common difference of pi or an algebraic expression etc.
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).

Lesson video

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6 Questions

Q1.
In the sequence $$3, 7, 11, 15, 19, ...$$ 'add four' is the __________.
term
$$n^\text{th}$$ term rule
Correct answer: term-to-term rule
solution
Q2.
What is the next term in this sequence? $$17, 23, 29, 35,$$
Correct Answer: 41
Q3.
What is the next term in this sequence? $$18, 11, 4, -3, ...$$
$$-4$$
$$-7$$
Correct answer: $$-10$$
$$-11$$
Q4.
What is the common additive difference in this sequence? $$4, -1, -6, -11, ...$$
$$+4$$
$$+5$$
$$-4$$
Correct answer: $$-5$$
$$-6$$
Q5.
What is the next term in this sequence? $$1, 3, 6, 10, 15, ...$$
Correct Answer: 21
Q6.
What is the $$10^\text{th}$$ term in this sequence? $$-11, -2, 7, 16, 25, ...$$
Correct Answer: 70

6 Questions

Q1.
$$4,5,7,8,10,11,13, ...$$ is not an arithmetic sequence because __________.
it does not have a common multiplicative difference between successive terms
it is linear
Correct answer: it does not have a common additive difference between successive terms
Q2.
What is the next term in this arithmetic sequence? $$7, 18, 29, ...$$
Correct Answer: 40
Q3.
What is the next term in this arithmetic sequence? $$41, 189, ...$$
Correct Answer: 337
Q4.
Which of these are arithmetic sequences?
$$x, 2x, 4x, 7x, ...$$
Correct answer: $${3\over7}, {6\over7}, {9\over7}, {12\over7}, ...$$
$${7\over3}, {7\over6}, {7\over9}, {7\over12}, ...$$
Correct answer: $$x, 3x+5, 5x+10, 7x+15, ...$$
Correct answer: $$-x, 2x, 5x, 8x, ...$$
Q5.
What is the $$n^\text{th}$$ term rule of this arithmetic sequence? $$9, 16, 23, 30, ...$$
$$n+7$$
$$7n$$
$$9n+7$$
$$7n+9$$
Correct answer: $$7n+2$$
Q6.
What is the $$n^\text{th}$$ term rule of this arithmetic sequence? $$1, 0.4, -0.2, -0.8, ...$$
$$1-6n$$
$$1-0.6n$$
$$n-0.6$$
Correct answer: $$1.6-0.6n$$