Checking and securing rules for generating arithmetic sequences | Maths

Starter quiz

In the sequence $3, 7, 11, 15, 19, ...$ 'add four' is the __________.

term

$n^\text{th}$ term rule

term-to-term rule ✓

solution
What is the next term in this sequence? $17, 23, 29, 35,$ ______

'41' ✓
What is the next term in this sequence? $18, 11, 4, -3, ...$

$-4$

$-7$

$-10$ ✓

$-11$
What is the common additive difference in this sequence? $4, -1, -6, -11, ...$

$+4$

$+5$

$-4$

$-5$ ✓

$-6$
What is the next term in this sequence? $1, 3, 6, 10, 15, ...$ ______

'21' ✓
What is the $10^\text{th}$ term in this sequence? $-11, -2, 7, 16, 25, ...$ ______

'70' ✓

$4,5,7,8,10,11,13, ...$ is not an arithmetic sequence because __________.

it does not have a common multiplicative difference between successive terms

it is linear

it does not have a common additive difference between successive terms ✓
What is the next term in this arithmetic sequence? $7, 18, 29, ...$ ______

'40' ✓
What is the next term in this arithmetic sequence? $41, 189, ...$ ______

'337' ✓
Which of these are arithmetic sequences?

$x, 2x, 4x, 7x, ...$

${3\over7}, {6\over7}, {9\over7}, {12\over7}, ...$ ✓

${7\over3}, {7\over6}, {7\over9}, {7\over12}, ...$

$x, 3x+5, 5x+10, 7x+15, ...$ ✓

$-x, 2x, 5x, 8x, ...$ ✓
What is the $n^\text{th}$ term rule of this arithmetic sequence? $9, 16, 23, 30, ...$

$n+7$

$7n$

$9n+7$

$7n+9$

$7n+2$ ✓
What is the $n^\text{th}$ term rule of this arithmetic sequence? $1, 0.4, -0.2, -0.8, ...$

$1-6n$

$1-0.6n$

$n-0.6$

$1.6-0.6n$ ✓

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The term-to-term rule is the common difference.
Finding the common difference can help when finding the n^th term rule.
Comparing the sequence to an appropriate multiplication table can help identify the translation that has been made.
The n^th term can be found for all arithmetic sequences.

Arithmetic sequences only have a positive integer as the common difference.

Arithmetic sequences can be increasing or decreasing and can have any value for the common difference.

Arithmetic sequence - An arithmetic (or linear) sequence is a sequence where the difference between successive terms is a constant.
N^th term - The n^th term of a sequence is the position of a term in a sequence where n stands for the term number.