Chapter 11 - Sequences; Induction; the Binomial Theorem - Section 11.3 Geometric Sequences; Geometric Series - 11.3 Assess Your Understanding - Page 844: 10

The sequence is geometric with a common ratio of $-5$. $s_1=-5$ $s_2=25$ $s_3=-125$ $s_4=625$

We need to substitute $1, 2, 3,$ and $4$ for $n$ into the given equation to find the first four terms. $s_1=(-5)^1=-5$ $s_2=(-5)^2=25$ $s_3=(-5)^3=(-5)(5)(5)=-125$ $s_4=(-5)^4=(5)(5)(5)(5)=625$ We see that the the next term is equal to $-5$ times the current term and this implies that the sequence is geometric with a common ratio of $-5$.