ExplicitSequence1

Sequences with Explicit Formulas

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

• Download file: File:Sequences2.txt (change the file extension from txt to pg when you save it)
• File location in NPL: NationalProblemLibrary/FortLewis/Authoring/Templates/IntegralCalc/Sequences2.pg

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PG problem file	Explanation
Problem tagging data	Problem tagging:
DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "AnswerFormatHelp.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]]; @seq = ( "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" ); $sequence = join(", ", @seq);	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. We create an array of strings @seq and use Perl's join function to paste the entries in this array together into one long string with entries separated by commas.
Context()->texStrings; BEGIN_TEXT Find a formula for \( n^{th} \) term of the sequence \( $sequence \). $BR $BR \( a_n = \) \{ ans_rule(20) \} \{ AnswerFormatHelp("formulas") \} END_TEXT Context()->normalStrings;	Main Text:
$showPartialCorrectAnswers = 1; ANS( $answer->cmp() );	Answer Evaluation:
Context()->texStrings; BEGIN_SOLUTION ${PAR}SOLUTION:${PAR} Solution explanation goes here. END_SOLUTION Context()->normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT();	Solution:

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