Find and use the formula for a geometric sequence

Error

There was an error loading the page.

Contributors

History

○

Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Find and use the formula for a geometric sequence.

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	3
r	integer	6
n	integer	6
nth_term	number	139968
b		Definition of variable `b` is empty.

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)" → "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

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

c)

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

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

$\begin{align} a_\var{n} &= \var{a} \times \var{r}^{\var{b}} \\ &= \var{a*r^n} \end{align}$

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

This question is not used in any exams.

Loading...

Error

Find and use the formula for a geometric sequence

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

Loading...

Error

Find and use the formula for a geometric sequence

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`