# 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.

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} = [,,,,,];

@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
Solution explanation goes here.
END_SOLUTION
Context()->normalStrings;

COMMENT('MathObject version.');

ENDDOCUMENT();


Solution: