Find and use the formula for a geometric sequence

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From users who are members of Transition to university :

Christian Lawson-Perfect	said	Ready to use	4 years, 4 months ago
Bradley Bush	said	Needs to be tested	7 years, 8 months ago
Hannah Aldous	said	Needs to be tested	7 years, 8 months ago
Lauren Richards	said	Has some problems	7 years, 8 months ago
Vicky Hall	said	Has some problems	7 years, 8 months ago

From users who are not members of Transition to university :

Ashley Cusack	said	Has some problems	4 years, 4 months ago
lucia ramsey	said	Ready to use	5 years, 10 months ago
Deirdre Casey	said	Has some problems	7 years, 4 months ago

History

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Christian Lawson-Perfect 4 years, 4 months ago

Saved a checkpoint:

I've fixed the advice for parts b and c - the power should be $n-1$ , not $n$ .

Restore this checkpoint

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Christian Lawson-Perfect 4 years, 4 months ago

Gave some feedback: Ready to use

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Ashley Cusack 4 years, 4 months ago

Gave some feedback: Has some problems

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Ashley Cusack commented 4 years, 4 months ago

Advice for parts B and C is incorrect.

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lucia ramsey 5 years, 10 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 4 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 4 months ago

Saved a checkpoint:

Looks like there was an off-by-one error.

Restore this checkpoint

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Deirdre Casey commented 7 years, 4 months ago

In part b does not accept correct answer. Mistake also shown in the solutions.

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Deirdre Casey 7 years, 4 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

Gave the variables sensible names and reworded some of the advice.

Restore this checkpoint

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Elliott Fletcher 7 years, 8 months ago

Published this.

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Bradley Bush 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Bradley Bush commented 7 years, 8 months ago

Splitting into 3 questions with 3 parts each instead of 3 parts with 3 gaps

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Christian Lawson-Perfect commented 7 years, 8 months ago

And like the other sequences questions, the advice would benefit hugely from a table.

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Christian Lawson-Perfect 7 years, 8 months ago

Gave some feedback: Has some problems

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Christian Lawson-Perfect 7 years, 8 months ago

Saved a checkpoint:

The gaps are all set as "mathematical expression", but there's no reason they shouldn't be "number entry" (apart from the formula part, obv.)

The parts of this question aren't coherent; you could keep the same sequence throughout, and ask the student to:

Find the common ratio

Give the formula for the $n$ th term

Calculate a given term.

Restore this checkpoint

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Lauren Richards commented 7 years, 8 months ago

Make sure i) and ii) etc are in italics both in the parts and the advice.

I think I would capitalise "Common ratio" in part a).

Advice content for a) is fine.

Where you have stated what the formula for the geometric sequence is in part b) of the advice, I think you should explain that a is the first term and r is the common ratio.

Make sure you use displaystyle to make the formula large.

Think there might be a slight glitch in the advice of c) where you are trying to figure out the common ratio, it says a[3]*a[4]^3 instead of 375 as it was supposed to be in this case.

Typo in the last sentence of the advice - it says "we can write substitute them into the formula..." - "We" should be capitalised and just scrap write.

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Lauren Richards 7 years, 8 months ago

Gave some feedback: Has some problems

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Vicky Hall commented 7 years, 8 months ago

It would also be helpful to give and exlain the formula for the $n$ th term in the statement.

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Vicky Hall 7 years, 8 months ago

Gave some feedback: Has some problems

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Vicky Hall commented 7 years, 8 months ago

I have added a sentence to the statement to explain what is meant by the common ratio. I think part a) should include one sequence with a positive integer ratio, one with a negative integer ratio and one with a fractional ratio to cover all possibilities.

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Hannah Aldous 7 years, 8 months ago

Gave some feedback: Needs to be tested

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Hannah Aldous 7 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Find and use the formula for a geometric sequence	Ready to use	Hannah Aldous	03/11/2020 14:54
Deirdre's copy of Find and use the formula for a geometric sequence	draft	Deirdre Casey	06/11/2017 12:40
Marte's copy of Find and use the formula for a geometric sequence	draft	Marte Bråtalien	12/04/2018 14:12
Joël's copy of Find and use the formula for a geometric sequence	draft	Jo Cohen	02/12/2020 15:42
Hallar el término general de una secuencia geométrica.	Ready to use	Luis Hernandez	02/12/2020 15:42
Simon's copy of Find and use the formula for a geometric sequence	draft	Simon Thomas	25/02/2019 10:50
Justin's copy of Find and use the formula for a geometric sequence	draft	Justin McGuinness	14/05/2019 15:02
Find and use the formula for a geometric sequence	draft	Xiaodan Leng	10/07/2019 21:48

There are 7 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	7
r	integer	4
n	integer	5
nth_term	number	7168

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(3..10 except r)

JME function reference

Description

The first term

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

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

→ Used by:

n
nth_term

Advice
"Part a)" - prompt
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer
"Part c)" → "Unnamed gap" - Minimum accepted value
"Part c)" → "Unnamed gap" - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
1. Step Information only
Part c) Gap-fill
1. Gap Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

Find the common ratio for the following geometric series.

$\var{a}, \var{a*r}, \var{a*r^2}, \var{a*r^3}, \ldots$

Common ratio: Unnamed gap

Advice

The terms in a geometric sequence are found by repeatedly multiplying the last term by a constant, called the common ratio.

a)

To find the common ratio, pick a term of the sequence and divide it by the previous term.

We can calculate the common ratio using a table:

$n$	$1$	$2$	$3$	$4$
$a_n$	$\var{a}$	$\var{a*r}$	$\var{a*r^2}$	$\var{a*r^3}$
$a_n \div a_{n-1}$		$\var{r}$	$\var{r}$	$\var{r}$

The common ratio is $\var{r}$ .

b)

The general formula for the $n^\text{th}$ term of a geometric sequence is

$\displaystyle {a_n=ar^{(n-1)}\text{,}}$

where $a$ is the first term, and $r$ is the common ratio.

So the formula for this sequence is

$a_n = \simplify[]{ {a}*{r}^(n-1) } \text{.}$

c)

We know from part b) that the formula for the $n^\text{th}$ term is $a_n = \simplify[]{ {a}*{r}^{(n-1)}}$ .

Therefore the $\var{n}^\text{th}$ term in the sequence is

$\begin{align} a_\var{n} &= \var{a} \times \var{r}^{\var{n-1}} \\ &= \var{a*r^(n-1)} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Find and use the formula for a geometric sequence

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Checkpoint description

Christian Lawson-Perfect 4 years, 4 months ago

Christian Lawson-Perfect 4 years, 4 months ago

Ashley Cusack 4 years, 4 months ago

Ashley Cusack commented 4 years, 4 months ago

lucia ramsey 5 years, 10 months ago

Christian Lawson-Perfect 7 years, 4 months ago

Christian Lawson-Perfect 7 years, 4 months ago

Deirdre Casey commented 7 years, 4 months ago

Deirdre Casey 7 years, 4 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Elliott Fletcher 7 years, 8 months ago

Bradley Bush 7 years, 8 months ago

Bradley Bush commented 7 years, 8 months ago

Christian Lawson-Perfect commented 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Christian Lawson-Perfect 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Lauren Richards commented 7 years, 8 months ago

Lauren Richards 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Vicky Hall 7 years, 8 months ago

Vicky Hall commented 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Hannah Aldous 7 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`