Hallar el término general de una secuencia geométrica.

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Luis Hernandez 6 years, 3 months ago

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Luis Hernandez 6 years, 3 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

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Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	10
r	integer	6
n	integer	4
nth_term	number	12960

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:

This variable doesn't seem to be used anywhere.

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.

Encontrar la razón común para la siguiente serie geométrica.

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

Razón común: 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.

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Mathematical expression
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Information only
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Number entry
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This question is used in the following exams:

4_MAT1407_C6_EJERCICIO_Numbas_9 by Luis Hernandez in MAt140_2020.
3_MAT1407_C6_EJERCICIO_Numbas_6 by Luis Hernandez in 2023_MAT1407.

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Hallar el término general de una secuencia geométrica.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Luis Hernandez 6 years, 3 months ago

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Hallar el término general de una secuencia geométrica.

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Luis Hernandez 6 years, 3 months ago

Luis Hernandez 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`