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