RecursiveSequence1
Sequences and Recursively Defined Functions
This PG code shows how to add a named function to the context and use it to ask students to come up with a recursive formula.
 File location in OPL: FortLewis/Authoring/Templates/Sequences/RecursiveSequence1.pg
 PGML location in OPL: FortLewis/Authoring/Templates/Sequences/RecursiveSequence1_PGML.pg
PG problem file  Explanation 

Problem tagging: 

DOCUMENT(); loadMacros( "PGstandard.pl", "MathObjects.pl", "parserFunction.pl", ); TEXT(beginproblem()); 
Initialization:
We will be defining a new named function and adding it to the context, and the easiest way to do this is using 
Context("Numeric")>variables>are(n=>"Real"); parserFunction(f => "sin(pi^n)+e"); $fn = Formula("3 f(n1) + 2"); 
Setup:
We define a new named function 
Context()>texStrings; BEGIN_TEXT The current value \( f(n) \) is three times the previous value, plus two. Find a recursive definition for \( f(n) \). Enter \( f_{n1} \) as \( f(n1) \). $BR \( f(n) \) = \{ ans_rule(20) \} END_TEXT Context()>normalStrings; 
Main Text: We should tell students to use function notation rather than subscript notation so that they aren't confused about syntax. 
$showPartialCorrectAnswers=1; ANS( $fn>cmp() ); 
Answer Evaluation: 
Context()>texStrings; BEGIN_SOLUTION Solution explanation goes here. END_SOLUTION Context()>normalStrings; COMMENT('MathObject version.'); ENDDOCUMENT(); 
Solution: 