Answer
The first five terms are:
$c_1 = 1;
\\c_2= -4;
\\c_3= 9;
\\c_4= -16;
\\c_5= 25$
Work Step by Step
For each term that is in the sequence, we plug in the given value for $n$:
$c_1 = (-1)^{1+1}(1^2) = (-1)^2(1) = 1(1) = 1;
\\c_2= (-1)^{2+1}(2^2) = (-1)^3(4) = -1(4) = -4;
\\c_3= (-1)^{3+1}(3^2) = (-1)^4(9) = 1(9) = 9;
\\c_4= (-1)^{4+1}(4^2) = (-1)^5(16) = -1(16) = -16;
\\c_5= (-1)^{5+1}(5^2) = (-1)^6(25) = 1(25) = 25$
