View of /trunk/NationalProblemLibrary/Rochester/setSequences4Arithmetic/ur_sq_4_5.pg

    1 ## DESCRIPTION
    2 ## Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('algebra','arithmetic sequence')
    6 ## Tagged by cmd6a 5/6/06
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Sequences and Series')
   10 ## DBsection('Arithmetic Sequences')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('Rochester')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGgraphmacros.pl"
   28 );
   29 
   30 TEXT(beginproblem());
   31 $showPartialCorrectAnswers = 1;
   32 
   33 $a = random(1,5,1);
   34 $b = $a + 1;
   35 $c = random(1,6,1);
   36 while ($c == $b) { $c = random(1,6,1);}
   37 $ansd = 1/$c;
   38 
   39 $ans1 = 1/$c - $a/$b;
   40 $ans2 = 2/$c - $a/$b;
   41 $ans3 = 3/$c - $a/$b;
   42 $ans4 = 4/$c - $a/$b;
   43 
   44 $RIGHT_BRACE = '\}';
   45 
   46 BEGIN_TEXT
   47 
   48 Find the common difference and write out the first four terms of the arithmetic sequence
   49 \( \displaystyle \left\{'\{'\} \frac{1}{$c} n-\frac{$a}{$b} \right${RIGHT_BRACE} \)
   50 
   51 Common difference is \{ans_rule(5)\}
   52 
   53 END_TEXT
   54 ANS(num_cmp($ansd, mode=>"arith"));
   55 
   56 BEGIN_TEXT
   57 
   58 \( a_1=\)\{ans_rule(7)\}, \( \ \ \) \( a_2=\)\{ans_rule(7)\}, \( \ \ \)
   59 \( a_3=\)\{ans_rule(7)\}, \( \ \ \) \( a_4=\)\{ans_rule(7)\}, \( \ \ \)
   60 
   61 END_TEXT
   62 ANS(num_cmp($ans1, mode=>"arith"));
   63 ANS(num_cmp($ans2, mode=>"arith"));
   64 ANS(num_cmp($ans3, mode=>"arith"));
   65 ANS(num_cmp($ans4, mode=>"arith"));
   66 
   67 
   68 ENDDOCUMENT();       # This should be the last executable line in the problem.