Try to answer the following questions here:

• What is this question used for?
• What does this question assess?
• What does the student have to do?
• How is the question randomised?
• Are there any implementation details that editors should be aware of?

### History and Feedback

#### Checkpoint description

Describe what's changed since the last checkpoint.

#### Martin Kilian6 months, 1 week ago

Gave some feedback: Ready to use

#### Luis Hernandez10 months, 3 weeks ago

Gave some feedback: Has some problems

#### Luis Hernandez10 months, 3 weeks ago

Gave some feedback: Ready to use

#### Christian Lawson-Perfect2 years, 3 months ago

Saved a checkpoint:

I don't think this question is worth saving. I've split part d, about finding a given term, into a separate question.

Ideally, there'd be a question combining parts a and b, asking you to sort a few sequences into linear, quadratic, geometric, or other.

I don't think there's any point in the parts which ask you to give the next three terms of the triangle, square, and cube numbers.

#### Christian Lawson-Perfect2 years, 3 months ago

Gave some feedback: Should not be used

Published this.

#### Bradley Bush2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Bradley Bush2 years, 4 months ago

Thank you for the feedback Christian:

• I have added tables to the feedback for parts and b to make the working easier to follow.
• I have added a table to the feedback for c also to analyse the difference between terms but I have included Hannahs solution using the formula as an alternative method of solving this.
• I have altered question d to be the more generic randomisable sequence equation which you suggested.
• I attempted to explain the solution using a table here to find the differences too but I am not too sure how thoroughly this would explain the way you work out that the sequence is squared numbers and cubic numbers without simply recognising them. Nor am I confident I even know how to recommend solving this problem if you do not recognise the squared or cubic terms on your own?

#### Christian Lawson-Perfect2 years, 4 months ago

Gave some feedback: Has some problems

#### Christian Lawson-Perfect2 years, 4 months ago

Saved a checkpoint:

Advice for part a could show each sequence with the common differences underneath, so it's easy to see which are linear. That's how I'd work it out.

Similarly with common ratios for part b.

For part c, I just use the fact that the difference between consecutive triangle numbers increases by 1 at each step. A drawing of the first few triangle numbers would help show this. While you can use the formula, it's not obvious, and you'd look at common differences first.

In part d, rather than using the triangle sequence in particular, I'd give a formula of the form $\frac{an(n+b)}{c}$ (what constraints are there on randomising this?) - you want to see that the student's comfortable with using a formula to get the nth term of a sequence without working out all the previous terms.

Part e relies on noticing that the sequences are the squares and cubes, respectively. How would you work this out? It's not enough to just state it in the advice. You might look at common differences, then make a guess that it's $n^2$ or $n^3$. The advice should show this experimental thinking - is it really $n^2$? How do we check? Draw a table of $n$ against $a_n$?

#### Hannah Aldous2 years, 4 months ago

Gave some feedback: Needs to be tested

#### Hannah Aldous2 years, 4 months ago

Created this as a copy of Finding the $n^{\text{th}}$ Term of a Quadratic Sequence.
Arithmetic sequences in an ice cream shop Ready to use Hannah Aldous 01/08/2017 13:41
Compute the partial sum of an arithmetic sequence Ready to use Hannah Aldous 01/08/2017 13:32
Finding the $n^{\text{th}}$ Term of a Quadratic Sequence Ready to use Hannah Aldous 01/08/2017 13:28
Identifying different types of sequences Ready to use Hannah Aldous 14/05/2019 14:52
Finding the formula for the $n^{\text{th}}$ term of linear sequences Ready to use Hannah Aldous 01/08/2017 13:40
Partial sum of an arithmetic sequence - birthday money Ready to use Hannah Aldous 01/08/2017 13:45
Find common difference in arithmetic sequences with gaps Ready to use Christian Lawson-Perfect 01/08/2017 13:56
Fill in the gaps in an arithmetic sequence Ready to use Christian Lawson-Perfect 01/08/2017 13:57
Write down and apply the formula for an arithmetic sequence. Ready to use Christian Lawson-Perfect 01/08/2017 13:57
Finding the Formula for the $n^{\text{th}}$ Term of Linear Sequences draft Chris Graham 20/07/2017 15:08
Inbbavathie's copy of Find common difference in arithmetic sequences with gaps draft Inbbavathie Ravi 24/07/2017 03:48
Find a particular term of a sequence using the given formula Ready to use Christian Lawson-Perfect 01/08/2017 13:31
Johan's copy of Write down and apply the formula for an arithmetic sequence. Has some problems Johan Maertens 02/08/2017 17:51
Finding the formula for the $n^{\text{th}}$ term of linear sequences draft steve kilgallon 19/11/2017 08:09
Compute the partial sum of an arithmetic sequence draft steve kilgallon 19/11/2017 08:11
Identifying different types of sequences draft Luis Hernandez 31/12/2018 01:38
Calcular la suma parcial de una sucesión aritmética Ready to use Luis Hernandez 14/01/2019 17:37
Identificando diferentes tipos de secuencias Ready to use Luis Hernandez 14/01/2019 13:19
Suma parcial de una secuencia aritmética - Cumpleaños Ready to use Luis Hernandez 14/01/2019 19:01
Encontrar la diferencia común en una Secuencia Aritmética Ready to use Luis Hernandez 14/01/2019 17:40
Encuentra un término particular de una secuencia usando la fórmula dada Ready to use Luis Hernandez 14/01/2019 17:48
Encontrar la fórmula para el término $n^{\text {th}}$ de una secuencia lineal Ready to use Luis Hernandez 14/01/2019 19:29
Simon's copy of Write down and apply the formula for an arithmetic sequence. draft Simon Thomas 25/02/2019 10:20
Simon's copy of Find common difference in arithmetic sequences with gaps draft Simon Thomas 25/02/2019 10:24
Simon's copy of Finding the formula for the $n^{\text{th}}$ term of linear sequences draft Simon Thomas 25/02/2019 10:30
Identifying different types of sequences draft Xiaodan Leng 10/07/2019 21:48
Write down and apply the formula for an arithmetic sequence. draft Xiaodan Leng 11/07/2019 01:48
Fill in the gaps in an arithmetic sequence draft Xiaodan Leng 11/07/2019 01:48
Find common difference in arithmetic sequences with gaps draft Xiaodan Leng 11/07/2019 01:49
Compute the partial sum of an arithmetic sequence draft Xiaodan Leng 11/07/2019 01:51
Partial sum of an arithmetic sequence - birthday money draft Xiaodan Leng 11/07/2019 01:54
Arithmetic sequences in an ice cream shop draft Xiaodan Leng 11/07/2019 01:55
Finding the formula for the $n^{\text{th}}$ term of linear sequences draft Xiaodan Leng 11/07/2019 01:55
Find a particular term of a sequence using the given formula draft Xiaodan Leng 11/07/2019 01:56
Finding the $n^{\text{th}}$ Term of a Quadratic Sequence draft Xiaodan Leng 11/07/2019 01:57
Paul's copy of Inbbavathie's copy of Find common difference in arithmetic sequences with gaps draft Paul Verheyen 05/10/2019 09:39

Give any introductory information the student needs.

No variables have been defined in this question.

(a number)

Numbers between and (inclusive) with step size
A random number between and (inclusive) with step size

(text string)

(numbers)

(text strings)

This variable is an HTML node. HTML nodes can not be relied upon to work correctly when resuming a session - for example, attached event callbacks will be lost, and mathematical notation will likely also break.

If this causes problems, try to create HTML nodes where you use them in content areas, instead of storing them in variables.

Describe what this variable represents, and list any assumptions made about its value.

This variable doesn't seem to be used anywhere.

Name Type Generated Value

#### Error in variable testing condition

There's an error in the condition you specified in the Variable testing tab. Variable values can't be generated until it's fixed.

Error:

for seconds

Running for ...

No parts have been defined in this question.

Select a part to edit.

The correct answer is an equation. Use the accuracy tab to generate variable values satisfying this equation so it can be marked accurately.

#### Checking accuracy

Define the range of points over which the student's answer will be compared with the correct answer, and the method used to compare them.

#### Variable value generators

Give expressions which produce values for each of the variables in the expected answer. Leave blank to pick a random value from the range defined above, following the inferred type of the variable.

#### String restrictions

Both choices and answers must be defined for this part.

Help with this part type

##### Base marking algorithm

#### Test that the marking algorithm works

Check that the marking algorithm works with different sets of variables and student answers using the interface below.

Create unit tests to save expected results and to document how the algorithm should work.

There's an error which means the marking algorithm can't run:

Name Value

Note
Value Feedback

Click on a note's name to show or hide it. Only shown notes will be included when you create a unit test.

#### Unit tests

No unit tests have been defined. Enter an answer above, select one or more notes, and click the "Create a unit test" button.

The following tests check that the question is behaving as desired.

### This test has not been run yet This test produces the expected output This test does not produce the expected output

This test is not currently producing the expected result. Fix the marking algorithm to produce the expected results detailed below or, if this test is out of date, update the test to accept the current values.

One or more notes in this test are no longer defined. If these notes are no longer needed, you should delete this test.

Name Value

 This note produces the expected output

This test has not yet been run.

When you need to change the way this part works beyond the available options, you can write JavaScript code to be executed at the times described below.

Run this script the built-in script.

This script runs after the built-in script.

To account for errors made by the student in earlier calculations, replace question variables with answers to earlier parts.

In order to create a variable replacement, you must define at least one variable and one other part.

The variable replacements you've chosen will cause the following variables to be regenerated each time the student submits an answer to this part:

These variables have some random elements, which means they're not guaranteed to have the same value each time the student submits an answer. You should define new variables to store the random elements, so that they remain the same each time this part is marked.

### Parts

Give a worked solution to the whole question.

### Preamble

This script will run after the question's variable have been generated but before the HTML is attached.
Apply styling rules to the question's content.

This question is used in the following exams: