Checking understanding of arithmetic sequences | Maths

Starter quiz

In the context of the arithmetic sequence 13, 20, 27, 34, 41, ..., you can call +7 the __________.
- addition
- $n^{th}$ term
- sum
- term-to-term rule ✓
Match each arithmetic (linear) sequence to its term-to-term rule.
- 1, 5, 9, 13, 17, ...
  
  ⇔
  
  +4 ✓
- -4, -1, 2, 5, 8, ...
  
  ⇔
  
  +3 ✓
- 2, -1, -4, -7, -10, ...
  
  ⇔
  
  -3 ✓
- 3, -4, -11, -18, -25, ...
  
  ⇔
  
  -7 ✓
- 3, 5, 7, 9, 11, ...
  
  ⇔
  
  +2 ✓
- -32, -25, -18, -11, -4, ...
  
  ⇔
  
  +7 ✓
Select the terms that are in this arithmetic sequence: 7, 15, 23, 31, ...
- $89$
- $87$ ✓
- $80$
- $55$ ✓
- $50$
Which of these terms are in the sequence described by "Start on 5 and add 3 each time"?
- 3
- 5 ✓
- 8 ✓
- 15
- 20 ✓
Select the expressions that have a value of 33 when $n=10$ .
- $4n-7$ ✓
- $33+n$
- $3n+3$ ✓
- $33n$
- $63-3n$ ✓
Find the value of the expression $9-6n$ when $n=4$ .
- -55
- -24
- -15 ✓
- 3
- 4

An $n^{\text{th}}$ term expression such as $7n-15$ is called a ...
- position-to-term rule ✓
- subtracting sequence
- term-to-term rule
- term-to-position rule
Which of the below are arithmetic sequences?
- 5, 10, 15, 20, 25, ... ✓
- 5, 10, 20, 40, ...
- 5, -5, -15, -25, ... ✓
- 5, 11, 18, 26, 35, ...
- 5, 12, 19, 26, 33, ... ✓
Match the $n^{\text{th}}$ term expression to the first term of the sequence.
- $6n+3$
  
  ⇔
  
  $9$ ✓
- $9n-5$
  
  ⇔
  
  $4$ ✓
- $4n+1$
  
  ⇔
  
  $5$ ✓
- $5n-3$
  
  ⇔
  
  $2$ ✓
- $2n-5$
  
  ⇔
  
  $-3$ ✓
- $9-3n$
  
  ⇔
  
  $6$ ✓
Which of the following are in the first five terms of the sequence $5n-4$ ?
- -4
- 1 ✓
- 5
- 9
- 16 ✓
Match each $n^{\text{th}}$ term expression to the $50^{\text{th}}$ term of the sequence. You may use a calculator.
- $2n-17$
  
  ⇔
  
  $83$ ✓
- $1.5n+7$
  
  ⇔
  
  $82$ ✓
- $0.6n+50$
  
  ⇔
  
  $80$ ✓
- $200-2.3n$
  
  ⇔
  
  $85$ ✓
- $234-3n$
  
  ⇔
  
  $84$ ✓
Which of these arithmetic sequences could be represented by this graph?
- 3, 8, 13, 18, 23, ...
- -3, -8, -13, -18, -23, ...
- -13, -8, -3, 2, 7, ...
- 8, 3, -2, -7, -12, ...
- 13, 8, 3, -2, -7, ... ✓

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An arithmetic sequence can be identified through a common difference between consecutive terms.
Arithmetic sequences can be represented visually as well as algebraically.
The formula for the n^th term allows us to generate any term in the sequence based on its position.

Pupils assume a sequence is arithmetic and only check the first few terms.

Encourage pupils to check all the terms of a sequence they are given to check that the pattern they think they have spotted is continuing.

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