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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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