Arithmetic sequences | Maths | Quizalize & Oak National Academy

Starter quiz

Which sequences have a constant additive pattern?
- 5, 6, 7, 8, ... ✓
- -8, 8, -8, 8, ...
- 1, 2, 4, 8, 16, ...
- 7, 9, 12, 16, ...
- 15, 11, 7, 3, ... ✓
Which sequences have a constant multiplicative pattern?
- 5, 10, 15, 20, ...
- 5, 10, 20, 40, ... ✓
- -2, 6, -18, 54, ... ✓
- 80, 40, 20, 10, ... ✓
- -4, 8, 16, 32, ...
Calculate the perimeter of this rectangle.
- '20 cm' ✓
Which of these is the area of this rectangle?
- 10 cm $^2$
- 20 cm $^2$
- 24 cm $^2$ ✓
- 36 cm $^2$
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
- add $6$ to the previous term ✓
- add $9$ to the previous term
- add $18$ to the previous term
What is the value of ${6\over 7} - 2{1\over2}$
- $-{23\over 14}$ ✓
- $-{1\over 5}$
- $-{1\over 14}$
- ${1\over 7}$
- $23\over 14$

Exit quiz

Match the keyword to its definition.
- arithmetic sequence
  
  ⇔
  
  a sequence that increases or decreases by the same step ✓
- common difference
  
  ⇔
  
  the constant additive rule from one term to the next ✓
- initial term
  
  ⇔
  
  the first term in a sequence ✓
- successive terms
  
  ⇔
  
  terms that are next to each other in a sequence ✓
Match the arithmetic sequences with their descriptions.
- 7, 5, 3, 1, ...
  
  ⇔
  
  initial term $7$ and common difference $-2$ ✓
- 7, 9, 11, 13, ...
  
  ⇔
  
  initial term $7$ and common difference $2$ ✓
- -1.6, -1.3, -1, -0.7, ...
  
  ⇔
  
  initial term $-1.6$ and common difference $0.3$ ✓
- -1.6, -1.9, -2.2, -2.5, ...
  
  ⇔
  
  initial term $-1.6$ and common difference $-0.3$ ✓
- -2, 3, 8, 13, ...
  
  ⇔
  
  fifth term $18$ and common difference $5$ ✓
- 38, 33, 28, 23, ...
  
  ⇔
  
  ninth term $-2$ and common difference $-5$ ✓
Which of these sequences are arithmetic?
- $7, 2, -3, -8, \;$ ... ✓
- $4, 1, -1, -4, \;$ ...
- $17, 24, 32, 39, \;$ ...
- ${4\over 5}, {1\over 2}, {1\over 5}, -{1\over 10}, \;$ ... ✓
- $-1, -2, -4, -8, \;$ ...
In which of these sequences do the number of shaded squares in each term form a linear sequence?
An arithmetic sequence has 3rd term = 41 and 7th term = 65. What is the initial term?
- '29' ✓
Which of these sequences are arithmetic?
- $a, 2a, 3a, 4a, \;$ ... ✓
- $a + 5, a + 8, a + 11, a + 14, \;$ ... ✓
- $a - 2b, a + b, a + 4b, a + 7b, \;$ ... ✓
- $5a + 3, 3a + 4, a + 5, 6-a, \;$ ... ✓
- $a, 2a + 4, 3a + 6, 4a + 8, \;$ ...

Worksheet

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Lesson Details

Key learning points

Finding the difference between each term can help you identify different types of sequence.
Sequences with a constant difference are arithmetic sequences.
Arithmetic sequences can be uniquely described with an initial term and a common difference.
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.