Geometric progression: The sum to infinity

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Simon Thomas 6 years, 1 month ago

Created this as a copy of Simon's copy of Geometric progression: The sum of the first n terms of a geometric progression.

Name	Status	Author	Last Modified
Arithmetic progression: The nth term of a series	Ready to use	Frank Doheny	20/03/2018 12:44
Arithmetic progression: The sum of the first n terms of a series	Ready to use	Frank Doheny	20/03/2018 12:44
Geometric progression: The nth term of a series	Ready to use	Frank Doheny	20/03/2018 08:28
Geometric progression: The sum of the first n terms of a geometric progression	Ready to use	Frank Doheny	20/03/2018 08:27
Andrew's copy of Arithmetic progression: The nth term of a series	draft	Andrew Dunbar	30/06/2017 22:04
Andrew's copy of Arithmetic progression: The sum of the first n terms of a series	draft	Andrew Dunbar	30/06/2017 22:04
Andrew's copy of Geometric progression: The nth term of a series	draft	Andrew Dunbar	30/06/2017 22:04
Simon's copy of Arithmetic progression: The nth term of a series	draft	Simon Thomas	25/02/2019 10:34
Simon's copy of Arithmetic progression: The sum of the first n terms of a series	draft	Simon Thomas	25/02/2019 10:36
Simon's copy of Geometric progression: The nth term of a series	draft	Simon Thomas	25/02/2019 10:55
Simon's copy of Geometric progression: The sum of the first n terms of a geometric progression	draft	Simon Thomas	25/02/2019 10:59
Geometric progression: The sum to infinity	draft	Simon Thomas	25/02/2019 11:23
Arithmetic progression: The nth term of a series	draft	Xiaodan Leng	10/07/2019 23:16
Arithmetic progression: The nth term of a series	draft	Xiaodan Leng	11/07/2019 00:22
Arithmetic progression: The sum of the first n terms of a series	draft	Xiaodan Leng	11/07/2019 00:23
Geometric progression: The nth term of a series	draft	Xiaodan Leng	11/07/2019 00:24
Geometric progression: The sum of the first n terms of a geometric progression	draft	Xiaodan Leng	11/07/2019 00:24

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Question statement

The first three terms of a geometric progression are given by:

$\var{a} + \simplify{{a}*{r}} + \simplify{{a}*{r}^2}\,+ \, ...........$

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	1
r	number	0.6
n	integer	4
s	number	2.5

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

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: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
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Gap-fill

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

Calculate the sum to infinity of the series.

$S_\infty=$ Unnamed gap

Advice

If the ratio between successive pairs of terms is a constant then the series under examination is a geometric progression.

Ths first term is $a$ and the common ratio is $r$ .

In this example $a=\var{a}$ , $r = \frac{\simplify{{a}*{r}}}{\var{a}}=\var{r}$ and $n = \var{n}$

Since $|r| = \var{r} < 1$ then the sum to infinity exists and can be calculated as:

$S_\infty=\frac{a}{1-r}$

So for our example:

$S_\infty=\frac{\var{a}}{1-\var{r}}$

$S_\var{n}=\var{precround(s,3)}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Arithmetic and Geometric Series by Simon Thomas in Maths support.
Sequences and series - Practice Exercise by Kwame D Dwamena in Kwame D's workspace.
Geometric sequence by Jinhua Mathias in Maths 3-2020.

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Taxonomy: mathcentre

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Simon Thomas 6 years, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Geometric progression: The sum to infinity

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`