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.

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.

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.

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).

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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: $$1.6-0.6n$$