Exercise 58 Page 320

Let's start by checking for a common ratio in the given sequence.

We see that there is common ratio of $\text{-}1,$ so it is a geometric sequence with first term $a_1=\text{-}5.$ Since it is geometric, we can represent it with a recursive rule. Let's write the recursive equation. The recursive rule for the sequence is $a_1=\text{-}5,a_n=\text{-}1\cdot a_{n-1}.$ Therefore, our friend's claim is not correct.