ExplicitSequence1
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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
| PG problem file | Explanation |
|---|---|
|
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. We create an array of strings |
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: |
