Chapter 12 - Sequences; Induction; the Binomial Theorem - 12.1 Sequences - 12.1 Assess Your Understanding - Page 807: 19

$a_1=1$ $a_2=-4$ $a_3=9$ $a_4=-16$ $a_5=25$

If $\{a_n\}=\left\{(-1)^{n+1}n^2\right\}$ then $a_1=(-1)^{1+1}1^2=(1)(1)=1$ $a_2=(-1)^{2+1}2^2=(-1)(4)=-4$ $a_3=(-1)^{3+1}3^2=(1)(9)=9$ $a_4=(-1)^{4+1}4^2=(-1)(16)=-16$ $a_5=(-1)^{5+1}5^2=(1)(25)=25$