Securing understanding of arithmetic sequences | Maths

Starter quiz

The arithmetic (linear) sequence 17, 21, 25, 29, 33, ... has a(n) _________ of +4.
- $n^{\text{th}}$ term
- $1^{\text{st}}$ term
- common difference ✓
- multiplier
Which of these sequences are arithmetic?
- 2, 6, 10, 14, ... ✓
- 2, 7, 12, 17, ... ✓
- 2, 8, 15, 23, ...
- 2, 4, 8, 16, ...
- 2, -1, -4, -7, ... ✓
Match the $n^{\text{th}}$ term to the first five terms of each sequence.
- $3n+2$
  
  ⇔
  
  $5, 8, 11, 14, 17, ...$ ✓
- $2n+3$
  
  ⇔
  
  $5, 7, 9, 11, 13, ...$ ✓
- $6n-1$
  
  ⇔
  
  $5, 11, 17, 23, 29, ...$ ✓
- $6-n$
  
  ⇔
  
  $5, 4, 3, 2, 1, ...$ ✓
- $5+n$
  
  ⇔
  
  $6, 7, 8, 9, 10, ...$ ✓
- $1-6n$
  
  ⇔
  
  $-5, -11, -17, -23, -29, ...$ ✓
The solution to the two-step equation $8x-13=83$ is $x=$ ______
- '12' ✓
Which is true of the solution to the equation $3x-10=3$
- It is a positive integer.
- It is a negative integer.
- It is non-integer. ✓
- It has no solution.
$8, 13, 18, 23, 28, ...$ are the first five terms of which sequence?
- $8n+5$
- $5n+8$
- $5n+3$ ✓
- $5n-3$

Exit quiz

In the $n^{\text{th}}$ term expression $9n-7$ , you call $9$ the __________ of $n$ .
- $1^{st}$ term
- coefficient ✓
- equation
- expression
What is the common difference in the arithmetic sequence $6n-3$ ?
- -6
- -3
- 3
- 6 ✓
Match each sequence to its $n^{\text{th}}$ term.
- $3n+9$
  
  ⇔
  
  $12, 15, 18, 21, 24, ...$ ✓
- $9n+3$
  
  ⇔
  
  $12, 21, 30, 39, 48, ...$ ✓
- $9n-3$
  
  ⇔
  
  $6, 15, 24, 33, 42, ...$ ✓
- $3n-9$
  
  ⇔
  
  $-6,-3,0,3,6, ...$ ✓
- $9-3n$
  
  ⇔
  
  $6,3,0,-3,-6, ...$ ✓
405 is a term in the arithmetic sequence with the rule $7n-50$ . What is its position in the sequence? $n=$ ______
- '65' ✓
Is $189$ a term in the arithmetic sequence $7n-50$ ?
- Yes, because $189$ is odd and the sequence contains a lot of odd numbers.
- Yes, because $189\div7=27$
- No, because $189$ is odd and the sequence is mostly even.
- No, because $7n-50=189$ has a non-integer solution. ✓
Which expressions could be used to generalise the arithmetic sequence 5, 9, 13, 17, 21, ...?
- $5n+4$
- $4n+1$ ✓
- $5+4n$
- $5+4(n-1)$ ✓
- $4+5(n-1)$

Worksheet

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Presentation

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Lesson Details

Key learning points

The n^th term is the generalised way of expressing any term in a sequence.
For an arithmetic sequence, it will have the form d(n-1)+a
The a refers to the first term of the sequence.
The d refers to the common difference between any two consecutive terms.

Common misconception

Misinterpreting the values in an expression for the n^th term. For example, given the n^th term $3n-5$ pupils may think that this relates to a sequence that is decreasing by 5 each time

Remind students about how the expression for the n^th term relates to multiples of a number (times tables) and then a shift. For example, 4, 9, 14, 19, ... can be seen as the 5 times table shifted down 1.

Keywords

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