Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.1 Sequences - 11.1 Assess Your Understanding - Page 827: 31

$\{a_n\}=(-1)^{n+1}$

We notice the pattern of the sequence that the sequence starts from $-1$ and then alternates the sign at each new term. So, we determine the pattern as: $$\{a_n\}=(-1)^{n+1}$$ Thus, we have $a_1=(-1)^{1+1}=(-1)^2=1$, $a_2=(-1)^{2+1}=(-1)^3=-1$, etc.