Geometric $\sum$ questions 2

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9 years, 7 months ago

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joshua boddy 9 years, 7 months ago

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joshua boddy 9 years, 8 months ago

Created this as a copy of Geometric

$\sum$ questions.

Name	Status	Author	Last Modified
Geometric $\sum$ questions	Ready to use	joshua boddy	01/06/2016 09:47
Geometric $\sum$ questions 2	Ready to use	joshua boddy	01/06/2016 09:47
Geometric $\sum$ questions 2	draft	Xiaodan Leng	11/07/2019 06:51
Geometric $\sum$ questions 2	draft	Xiaodan Leng	11/07/2019 06:52

Question statement

For the following geometric series

Give any introductory information the student needs.

			Name	Type	Generated Value

upsum	integer	14
mult	integer	2
num	integer	5
denom	integer	3
r	rational	5/3
mult2	integer	3
r2	integer	2

Automatically regenerate variables?

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Value

xxxxxxxxxx
 
random(10..20)

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Description

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

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

Parts

Gap-fill

Gap-fill

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

For $\sum\limits_{i=0}^\var{upsum} \frac{1}{\var{mult2}} \times (\var{r2})^{i}$

What is the first term? Gap 0.

What is the common ratio? Gap 1.

What is the value of the sum? Gap 2.

Advice

We will look at solutions for a). The method for b) is exactly the same.

To find the first term, plug in i=0. That is $\frac{1}{\var{mult2}} \times (\var{r2})^{0}=\frac{1}{\var{mult2}}\times 1 = \frac{1}{\var{mult2}}$

To find the common ratio, we look at the $(i+1)$ ^thterm divided by the $i$ ^th term. That is $\frac{\frac{1}{\var{mult2}}\times \simplify{{r2}}^{i}}{\frac{1}{\var{mult2}}\times \simplify{{r2}}^{i-1}} = \var{r2}$

To find the value of the sum, we apply the known formula for a geometric series for finding the sum of the first $n$ terms. That is $S_n = \frac{a_1(1-r^n)}{1-r}$ , where $a_1$ is the first term and $r$ is the common ratio. In our case we have $S_n = \frac{\frac{1}{\var{mult2}}(1-\var{r2}^n)}{1-\var{r2}}$

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joshua boddy 9 years, 7 months ago

joshua boddy 9 years, 8 months ago

Error in variable testing condition

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Generated value: `integer`

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Geometric ∑\sum questions 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

joshua boddy 9 years, 7 months ago

joshua boddy 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Geometric $\sum$ questions 2

Generated value: `integer`