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

Mon May 8 17:05:32 2006 UTC (7 years ago) by jjholt
File size: 1481 byte(s)
Added tags.


    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
23 "PG.pl",
24 "PGbasicmacros.pl",
25 "PGchoicemacros.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.