Geometric progression: The sum of the first n terms of a geometric progression

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Frank Doheny

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7 years ago

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Frank Doheny 7 years ago

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Frank Doheny 8 years, 4 months ago

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Frank Doheny 8 years, 4 months ago

Created this as a copy of Geometric progression: The nth term of a series.

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 series 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	6
r	number	2.2
n	integer	19
s	number	16032483.606509203

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`

→ Used by:

Statement
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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 of the first $\var{n}$ terms of the series.

$S_\var{n}=$ 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 $r$ .

The formula for the sum of the first $n$ terms of the series is given by: $S_n=\frac{a(1-r^{n})}{1-r}$

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

$S_\var{n}=\frac{\var{a}(1-(\var{r})^{\var{n}})}{1-\var{r}}$

$S_\var{n}=\frac{\var{a}*(\simplify{1-{r}^{n}})}{\simplify{1-{r}}}$

$S_\var{n}=\frac{\simplify{{a}*(1-{r}^{n})}}{\simplify{1-{r}}}$

$S_\var{n}=\var{s}$

Give a worked solution to the whole question.

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Part	Test	Passed?
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Number entry		Hasn't run yet

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Geometric progression: The sum of the first n terms of a geometric progression

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Taxonomy: mathcentre

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Checkpoint description

Frank Doheny 7 years ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

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Error

Geometric progression: The sum of the first n terms of a geometric progression

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Frank Doheny 7 years ago

Frank Doheny 8 years, 4 months ago

Frank Doheny 8 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`