Difference between revisions of "ExplicitSequence1"

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(add historical tag and give links to newer problems.)
 
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{{historical}}
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<p style="font-size: 120%;font-weight:bold">This problem has been replaced with [https://openwebwork.github.io/pg-docs/sample-problems/Sequences/ExplicitSequence.html a newer version of this problem]</p>
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<h2>Sequences with Explicit Formulas</h2>
  
<h2>Sequences with Explicit Formulas</h2>
   
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[[File:Sequences2.png|300px|thumb|right|Click to enlarge]]
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[[File:ExplicitSequence1.png|300px|thumb|right|Click to enlarge]]
 
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
  
<p style="background-color:#f9f9f9;border:black solid 1px;padding:3px;">
 
This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.
  
This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.
 
</p>
  
</p>
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* Download file: [[File:Sequences2.txt]] (change the file extension from txt to pg when you save it)
  
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<!--* File location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1.pg]-->
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* File location in NPL: <code>FortLewis/Authoring/Templates/IntegralCalc/Sequences2.pg</code>
  
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* PGML location in OPL: [https://github.com/openwebwork/webwork-open-problem-library/blob/master/OpenProblemLibrary/FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg]
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<br clear="all" />
  
<br clear="all" />
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<tr valign="top">
  
<tr valign="top">
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<th> PG problem file </th>
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<th style="width: 50%"> PG problem file </th>
 
<th> Explanation </th>
  
<th> Explanation </th>
 
</tr>
  
</tr>
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DOCUMENT();
  
DOCUMENT();
   
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loadMacros(
  
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loadMacros('PGstandard.pl','MathObjects.pl','PGML.pl','PGcourse.pl');
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"PGstandard.pl",
  
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"MathObjects.pl",
  
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"AnswerFormatHelp.pl",
  
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);
  
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TEXT(beginproblem());
  
TEXT(beginproblem());
 
</pre>
  
</pre>
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<td style="background-color:#ffffdd;border:black 1px dashed;">
  
<td style="background-color:#ffffdd;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context("Numeric");
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Context('Numeric');
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Context()->variables->are(n=>"Real");
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Context()->variables->are(n=>'Real');
   
 
$answer = Compute("(-1)^n / n!");
  
$answer = Compute("(-1)^n / n!");
 
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];
  
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];
   
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@seq = (
  
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$sequence = 'a_0=1, a_1 = -1, a_2 = \frac{1}{2}, a_3 = -\frac{1}{6}'
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"a_0 = 1",
  
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. 'a_4 = \frac{1}{24}, a_5 = -\frac{1}{120}, \ldots';
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"a_1 = -1",
  
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"a_2 = \frac{1}{2}",
  
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"a_3 = -\frac{1}{6}",
  
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"a_4 = \frac{1}{24}",
  
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"a_5 = -\frac{1}{120}",
  
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"\ldots"
  
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);
  
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$sequence = join(", ", @seq);
  
 
</pre>
  
</pre>
 
</td>
  
</td>
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<b>Setup:</b>
 
<b>Setup:</b>
 
We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as <code>cos(pi * n) / n!</code>, you should still restrict the domain to positive integers, because some students may simplify this to <code>(-1)^n / n!</code> and receive errors because the answer checker is substituting things such as <code>n=0.5</code> into their formula.
  
We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as <code>cos(pi * n) / n!</code>, you should still restrict the domain to positive integers, because some students may simplify this to <code>(-1)^n / n!</code> and receive errors because the answer checker is substituting things such as <code>n=0.5</code> into their formula.
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</p>
  
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<p>
  
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We create an array of strings <code>@seq</code> and use Perl's join function to paste the entries in this array together into one long string with entries separated by commas.
  
 
</p>
  
</p>
 
</td>
  
</td>
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<td style="background-color:#ffdddd;border:black 1px dashed;">
  
<td style="background-color:#ffdddd;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
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BEGIN_PGML
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BEGIN_TEXT
  
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Find a formula for [` n^{th} `] term of the sequence [` [$sequence] `].
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Find a formula for \( n^{th} \) term of the sequence \( $sequence \).
  
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$BR
  
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[` a_n = `] [__________________]{$answer}
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$BR
  
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\( a_n = \)
  
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[@ helpLink('formulas') @]*
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\{ ans_rule(20) \}
  
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END_PGML
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\{ AnswerFormatHelp("formulas") \}
  
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END_TEXT
  
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Context()->normalStrings;
  
 
</pre>
  
</pre>
 
<td style="background-color:#ffcccc;padding:7px;">
  
<td style="background-color:#ffcccc;padding:7px;">
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</td>
  
</td>
 
</tr>
  
</tr>
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<!-- Answer evaluation section -->
  
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<tr valign="top">
  
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<td style="background-color:#eeddff;border:black 1px dashed;">
  
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<pre>
  
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$showPartialCorrectAnswers = 1;
  
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ANS( $answer->cmp() );
  
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</pre>
  
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<td style="background-color:#eeccff;padding:7px;">
  
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<p>
  
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<b>Answer Evaluation:</b>
  
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</p>
  
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</td>
  
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</tr>
  
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<!-- Solution section -->
  
<!-- Solution section -->
   
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<td style="background-color:#ddddff;border:black 1px dashed;">
  
<td style="background-color:#ddddff;border:black 1px dashed;">
 
<pre>
  
<pre>
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Context()->texStrings;
  
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BEGIN_PGML_SOLUTION
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BEGIN_SOLUTION
  
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${PAR}SOLUTION:${PAR}
  
 
Solution explanation goes here.
  
Solution explanation goes here.
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END_SOLUTION
  
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END_PGML_SOLUTION
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Context()->normalStrings;
  
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COMMENT('MathObject version.');
  
   
 
ENDDOCUMENT();
  
ENDDOCUMENT();
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[[Category:Top]]
  
[[Category:Top]]
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[[Category:Authors]]
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[[Category:Sample Problems]]
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[[Category:Subject Area Templates]]

Latest revision as of 06:44, 18 July 2023

This article has been retained as a historical document. It is not up-to-date and the formatting may be lacking. Use the information herein with caution.

This problem has been replaced with a newer version of this problem

Sequences with Explicit Formulas

Click to enlarge

This PG code shows how to evaluate answers that are (possibly alternating) sequences with explicit formulas.


Templates by Subject Area

PG problem file Explanation

Problem tagging data

Problem tagging: 

DOCUMENT();

loadMacros('PGstandard.pl','MathObjects.pl','PGML.pl','PGcourse.pl');
TEXT(beginproblem());

Initialization: 

Context('Numeric');
Context()->variables->are(n=>'Real');

$answer = Compute("(-1)^n / n!");
$answer->{test_points} = [[1],[2],[3],[4],[5],[6]];

$sequence = 'a_0=1, a_1 = -1, a_2 = \frac{1}{2}, a_3 = -\frac{1}{6}'
  . 'a_4 = \frac{1}{24}, a_5 = -\frac{1}{120}, \ldots';

Setup: We set the test points to be positive integers to avoid errors when evaluating the answer. Even if you expect students to enter answers such as cos(pi * n) / n!, you should still restrict the domain to positive integers, because some students may simplify this to (-1)^n / n! and receive errors because the answer checker is substituting things such as n=0.5 into their formula. 

BEGIN_PGML
Find a formula for [` n^{th} `] term of the sequence [` [$sequence] `].

[` a_n = `] [__________________]{$answer}

[@ helpLink('formulas') @]*
END_PGML

Main Text: 

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution:

Templates by Subject Area

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