ExplicitSequence1

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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.

• PGML location in OPL: FortLewis/Authoring/Templates/Sequences/ExplicitSequence1_PGML.pg

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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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