New
New
Year 8

Arithmetic sequences

I can appreciate the features of an arithmetic sequence and be able to recognise one.

New
New
Year 8

Arithmetic sequences

I can appreciate the features of an arithmetic sequence and be able to recognise one.

Lesson details

Key learning points

1. Finding the difference between each term can help you identify different types of sequence.
2. Sequences with a constant difference are arithmetic sequences.
3. Arithmetic sequences can be uniquely described with an initial term and a common difference.
4. It is possible to identify which sequences are arithmetic.

Common misconception

Sequences such as triangular numbers which have a linear sequence in their differences are linear.

Terms in an arithmetic sequence have to have a common first difference.

Keywords

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

Pupils will come across arithmetic and linear in different topics, use both words so links can be drawn to linear equations and linear graphs.
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.
Which sequences have a constant additive pattern?
Correct answer: 5, 6, 7, 8, ...
-8, 8, -8, 8, ...
1, 2, 4, 8, 16, ...
7, 9, 12, 16, ...
Correct answer: 15, 11, 7, 3, ...
Q2.
Which sequences have a constant multiplicative pattern?
5, 10, 15, 20, ...
Correct answer: 5, 10, 20, 40, ...
Correct answer: -2, 6, -18, 54, ...
Correct answer: 80, 40, 20, 10, ...
-4, 8, 16, 32, ...
Q3.
Calculate the perimeter of this rectangle.
Q4.
Which of these is the area of this rectangle?
10 cm$$^2$$
20 cm$$^2$$
Correct answer: 24 cm$$^2$$
36 cm$$^2$$
Q5.
What is the term-to-term rule for a sequence with a constant additive pattern which has first term = 23 and 4th term = 41.
add $$2$$ to the previous term
add $$4.5$$ to the previous term
Correct answer: add $$6$$ to the previous term
add $$9$$ to the previous term
add $$18$$ to the previous term
Q6.
What is the value of $${6\over 7} - 2{1\over2}$$
Correct answer: $$-{23\over 14}$$
$$-{1\over 5}$$
$$-{1\over 14}$$
$${1\over 7}$$
$$23\over 14$$

Exit quiz

6 Questions

Q1.
Match the keyword to its definition.
Correct Answer:arithmetic sequence,a sequence that increases or decreases by the same step

a sequence that increases or decreases by the same step

Correct Answer:common difference,the constant additive rule from one term to the next

the constant additive rule from one term to the next

Correct Answer:initial term,the first term in a sequence

the first term in a sequence

Correct Answer:successive terms,terms that are next to each other in a sequence

terms that are next to each other in a sequence

Q2.
Match the arithmetic sequences with their descriptions.
Correct Answer:7, 5, 3, 1, ...,initial term $$7$$ and common difference $$-2$$

initial term $$7$$ and common difference $$-2$$

Correct Answer:7, 9, 11, 13, ...,initial term $$7$$ and common difference $$2$$

initial term $$7$$ and common difference $$2$$

Correct Answer:-1.6, -1.3, -1, -0.7, ...,initial term $$-1.6$$ and common difference $$0.3$$

initial term $$-1.6$$ and common difference $$0.3$$

Correct Answer:-1.6, -1.9, -2.2, -2.5, ...,initial term $$-1.6$$ and common difference $$-0.3$$

initial term $$-1.6$$ and common difference $$-0.3$$

Correct Answer:-2, 3, 8, 13, ...,fifth term $$18$$ and common difference $$5$$

fifth term $$18$$ and common difference $$5$$

Correct Answer:38, 33, 28, 23, ...,ninth term $$-2$$ and common difference $$-5$$

ninth term $$-2$$ and common difference $$-5$$

Q3.
Which of these sequences are arithmetic?
Correct answer: $$7, 2, -3, -8, \;$$...
$$4, 1, -1, -4, \;$$...
$$17, 24, 32, 39, \;$$...
Correct answer: $${4\over 5}, {1\over 2}, {1\over 5}, -{1\over 10}, \;$$...
$$-1, -2, -4, -8, \;$$...
Q4.
In which of these sequences do the number of shaded squares in each term form a linear sequence?
Correct Answer: An image in a quiz
Correct Answer: An image in a quiz
Q5.
An arithmetic sequence has 3rd term = 41 and 7th term = 65. What is the initial term?
Correct answer: $$a, 2a, 3a, 4a, \;$$...
Correct answer: $$a + 5, a + 8, a + 11, a + 14, \;$$...
Correct answer: $$a - 2b, a + b, a + 4b, a + 7b, \;$$...
Correct answer: $$5a + 3, 3a + 4, a + 5, 6-a, \;$$...
$$a, 2a + 4, 3a + 6, 4a + 8, \;$$...