Conditions in arithmetic sequences | Maths | Quizalize & Oak National Academy

Starter quiz

$6n-7$ is the __________ of the arithmetic sequence starting $-1, 5, 11, 17, 23, ...$

position-to-term rule ✓

term-to-term rule

$n^\text{th}$ term rule ✓

term value
What is the $n^\text{th}$ term rule of the sequence $14,22,30,38,46, ...$ ?

$n+14$

$n+8$

$14+8n$

$14n+8$

$8n+6$ ✓
What is the $n^\text{th}$ term rule of the sequence $197,191,185,179,173, ...$ ?

$n-6$

$197n-6$

$197-6n$

$203-6n$ ✓

$203n-6$
What is the $40^\text{th}$ term of the sequence $9n+51$ ?

'411' ✓
What position is $213$ in the following arithmetic sequence? $18,23,28,33, ...$

'40' ✓
Solve the equation $8n-37=495$ If necessary leave your answer as a decimal. $n=$ ______

'66.5' ✓

$5n-28=100$ is __________ we can solve in order to help us find the first term over $100$

an expression

a solution

an equation ✓

a term-to-term rule
Using trial and error, which is the best estimate at which to start to find the first value over $1000$ in the sequence starting $-17,-13,-9,-5,-1, ...$ ?

$n=10$

$n=100$

$n=1000$

$n=25$

$n=250$ ✓
If you open a savings account with $\pounds50$ and put $\pounds8$ a week in to the account every week thereafter without withdrawing anything, after how many weeks will you reach $\pounds200$ ?

4 weeks

19 weeks ✓

20 weeks

25 weeks
Which term is the first value below $−300$ in the arithmetic sequence starting $91, 83, 75, 67, 59, …$ ?

The $47^\text{th}$ term

The $48^\text{th}$ term

The $49^\text{th}$ term

The $50^\text{th}$ term ✓

The $51^\text{st}$ term
The solution to $2n-19=98$ is $n=58.5$ What does this tell us about this sequence? $-17,-15,-13,-11, ...$

The $58.5^\text{th}$ term is $98$

The $58^\text{th}$ term is above $98$

The $59^\text{th}$ term is above $98$ ✓
What is the last positive value in the sequence $380, 365, 350, 335, ...$ ?

$n=26$

$5$ ✓

$n=27$

$10$

Loading worksheet ...

Loading presentation ...

The n^th term rule can calculate the position of the value that is equal to the given value.
If this is not an integer, then you can round down or up as needed.
This term number can be used to generate the desired value.

Pupils may round the wrong way when finding the term number for a particular term value.

By calculating the terms either side of the non-integer value of $n$ , pupils can easily determine what the rounded value of $n$ should be.

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.