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

Error

There was an error loading the page.

Contributors

Frank Doheny

Feedback

From users who are members of Series :

Frank Doheny

said

Ready to use

7 years, 1 month ago

History

○

Frank Doheny 7 years, 1 month ago

Gave some feedback: Ready to use

○

Frank Doheny 8 years, 5 months ago

Published this.

○

Frank Doheny 8 years, 5 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

There are 15 other versions that do you not have access to.

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	2
r	number	2.4
n	integer	6
s	number	271.57568

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:

This variable doesn't seem to be used anywhere.

Parts

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.

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.

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

This question is used in the following exams:

Series quiz by Frank Doheny in Series.
Angharad's copy of Series quiz by Angharad Thomas in Angharad Old Stuff.
Foundation Maths Test 1819 by Paul Molloy in Paul's workspace.
Series and Sequences MHB + MSB by Max S in Max's workspace.
Sequences & Series Quiz by Kevin Bohan in Kevin's workspace.
Sequences and series - Practice Exercise by Kwame D Dwamena in Kwame D's workspace.
Sequences and Series quiz by Stephen Maher in Stephen's workspace.
Blathnaid's copy of Series quiz by Blathnaid Sheridan in Blathnaid's workspace.
Arithmetic & Geometric Series by Michael Proudman in .Algebra.
Wenling's copy of Series quiz by Wenling Zhang in Wenling's workspace.
Series quiz short by claire lines in claire's workspace.
Week 16 e-quiz by Ruth Douglas in Ruth's workspace.
Series quiz long by claire lines in claire's workspace.
David's copy of Series quiz by David Elliott-Button in David's workspace.
Arithmetic and Geometric Series Quiz by Maryam Kashia Garba in Maryam Kashia's workspace.
Shweta's copy of Arithmetic and Geometric Series Quiz by Shweta Sharma in Shweta's workspace.

Loading...

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, 1 month ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

Loading...

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, 1 month ago

Frank Doheny 8 years, 5 months ago

Frank Doheny 8 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`