Encontrar la fórmula para el término $n^{\text {th}}$ de una secuencia lineal

Error

There was an error loading the page.

Contributors

Feedback

From users who are members of Progresiones Aritméticas :

Luis Hernandez

said

Ready to use

6 years, 2 months ago

History

○

Luis Hernandez 6 years, 2 months ago

Gave some feedback: Ready to use

○

Luis Hernandez 6 years, 2 months ago

Created this as a copy of Finding the formula for the

$n^{\text{th}}$ term of linear sequences.

Name	Status	Author	Last Modified
Arithmetic sequences in an ice cream shop	Ready to use	Hannah Aldous	20/11/2019 14:36
Compute the partial sum of an arithmetic sequence	Ready to use	Hannah Aldous	20/11/2019 14:36
Finding the $n^{\text{th}}$ Term of a Quadratic Sequence	Ready to use	Hannah Aldous	20/11/2019 14:39
Identifying different types of sequences	Should not be used	Hannah Aldous	01/12/2020 16:24
Finding the formula for the $n^{\text{th}}$ term of linear sequences	Ready to use	Hannah Aldous	20/11/2019 14:39
Partial sum of an arithmetic sequence - birthday money	Ready to use	Hannah Aldous	20/11/2019 14:41
Find common difference in arithmetic sequences with gaps	Ready to use	Christian Lawson-Perfect	20/11/2019 14:39
Fill in the gaps in an arithmetic sequence	Ready to use	Christian Lawson-Perfect	20/11/2019 14:39
Write down and apply the formula for an arithmetic sequence.	Ready to use	Christian Lawson-Perfect	20/11/2019 14:46
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	20/11/2019 14:38
Johan's copy of Write down and apply the formula for an arithmetic sequence.	Has some problems	Johan Maertens	02/08/2017 17:51
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	02/12/2020 15:42
Identificar diferentes tipos de sucesiones...	Ready to use	Luis Hernandez	02/11/2020 02:05
Suma parcial de una secuencia aritmética - Cumpleaños	Ready to use	Luis Hernandez	02/12/2020 15:42
Encontrar la diferencia común en una Secuencia Aritmética	Ready to use	Luis Hernandez	02/12/2020 15:42
Encontrar el término de una sucesión usando la fórmula dada...	Ready to use	Luis Hernandez	02/12/2020 15:42
Encontrar la fórmula para el término $n^{\text {th}}$ de una secuencia lineal	Ready to use	Luis Hernandez	02/12/2020 15:42
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
Ugur's copy of Write down and apply the formula for an arithmetic sequence.	Ready to use	Ugur Efem	12/01/2022 11:45

There are 47 other versions that do you not have access to.

Question statement

Una secuencia lineal es una serie de números que aumenta o disminuye en una cantidad constante en cada paso.

Encuentre fórmulas para el término $n^ {\text{th}}$ para cada una de las siguientes secuencias lineales, donde se dan los valores para $n = 1 \text {,} 2 \text {,}3$ :

Give any introductory information the student needs.

			Name	Type	Generated Value

m	list	[ 8, 9, 2, 5, 5 ]
n	list	[ 1, 1, 1, 3, 4, 4, 2 ]
c	list	[ 8, 12, 5, 11, 7, 13, 6, 6 ]
ci	list	List of 10 items
ni	list	List of 10 items
b	list	[ 2, 3, 3, 4, 3 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(2..10),5)

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `list`

[ 8, 9, 2, 5, 5 ]

→ Used by:

Advice
"Part a)" - prompt
"Part a)" → "Unnamed gap" - Correct answer
"Part a)" → "Step 0." - Minimum accepted value
"Part a)" → "Step 0." - Maximum accepted value
"Part a)" → "Step 1." - Minimum accepted value
"Part a)" → "Step 1." - Maximum accepted value
"Part b)" - prompt
"Part b)" → "Unnamed gap" - Correct answer
"Part b)" → "Step 0." - Minimum accepted value
"Part b)" → "Step 0." - Maximum accepted value

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\var{m[1]*2}, \var{m[1]*3}, \var{m[1]*4}, \ldots$

Término de lugar $n^\text{th}$ = Unnamed gap

Advice

Ambas secuencias son lineales o aritméticas. Para encontrar fórmulas para estas secuencias necesitamos identificar sus primeros términos y diferencias comunes..

a)

La fórmula para el término $n^\text {th}$ de una secuencia aritmética es: $a_n = a_1 + (n-1) d \text {.}$

$a_1$ es el primer término y $d$ la diferencia común entre términos consecutivos, que debemos identificar.

Podemos encontrarlos dibujando una tabla de $a_n$ contra $n$ , y las diferencias entre términos consecutivos.

$n$	1	2	3
$a_n$	$\pmb{\var{m[1]*2}}$	$\var{m[1]*3}$	$\var{m[1]*4}$
Primeras diferencias		$\pmb{\var{m[1]}}$	$\pmb{\var{m[1]}}$

El primer término y la diferencia común se han resaltado en negrita; Podemos usar estos para escribir la fórmula de la secuencia.

$\begin{align} a_n &= a_1+(n-1)d \\ &= \var{m[1]*2}+(n-1)\times\var{m[1]} \\ &= \var{m[1]}n + \var{m[1]}\text{.} \end{align}$

b)

De manera similar a la parte a), podemos identificar $a_1$ y $d$ para esta secuencia dibujando una tabla de $a_n$ contra $n$ .

$a_n$	$\pmb{\var{m[2]*8+2}}$	$\simplify{{m[2]}*7+2}$	$\simplify{{m[2]}*6+2}$
Primeras diferencias		$\pmb{\var{-m[2]}}$	$\pmb{\var{-m[2]}}$

El primer término y la diferencia común se han resaltado en negrita; Podemos usar estos para formar la fórmula para la secuencia.

$\begin{align} a_n &=a_1+(n-1)d \\ &=\var{m[2]*8+2}+(n-1)\times\var{-m[2]} \\ &=-\var{m[2]}n + \var{m[2]*9+2}\text{.} \end{align}$

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
Mathematical expression
Mathematical expression		Hasn't run yet
Information only
Number entry
Number entry		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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Examen Progresiones aritméticas by Luis Hernandez in Progresiones Aritméticas.

Loading...

Error

Encontrar la fórmula para el término $n^{\text {th}}$ de una secuencia lineal

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Luis Hernandez 6 years, 2 months ago

Luis Hernandez 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

Loading...

Error

Encontrar la fórmula para el término nthn^{\text {th}} de una secuencia lineal

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Luis Hernandez 6 years, 2 months ago

Luis Hernandez 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

Encontrar la fórmula para el término $n^{\text {th}}$ de una secuencia lineal

Generated value: `list`