ExplicitSequence1

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Revision as of 10:55, 4 April 2023 by Pstaabp (talk | contribs) (switch to PGML and remove answerFormatHelp.pl macro)
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Sequences with Explicit Formulas

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


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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:

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