##DESCRIPTION
##KEYWORDS('')
##
##ENDDESCRIPTION

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGgraphmacros.pl"
);

TEXT(beginproblem());
$showPartialCorrectAnswers = 1;

$a = random(3,5,1);
$b = random(-5,10);
$c = random(1,3,1);

if ($a == 3) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + 4*$b;}
if ($a == 4) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + ($c+4)**2 + 5*$b;}
if ($a == 5) {$ans = $c**2 - ($c+1)**2 + ($c+2)**2 - ($c+3)**2 + ($c+4)**2 - ($c+5)**2 + 6*$b;}

BEGIN_TEXT
Evaluate the sum:
\[ \sum_{k=0}^{$a}{((-1)^k (k+$c)^2+$b)} \]
\{ans_rule(20)\}

END_TEXT
ANS(num_cmp($ans, mode=>"arith"));

ENDDOCUMENT();       # This should be the last executable line in the problem.