Question

1. what is the common ratio in this recursive definition?

$a_1 = 4$
$a_n = -1.5a_{n - 1}$
$a_{n - 1}$?
$r = -1.5$
$r = 4$
$r = 1.5$

Explanation:

Step1: Recall geometric sequence recursion

A geometric sequence recursive formula is $a_n = r \cdot a_{n-1}$, where $r$ is the common ratio.

Step2: Match given formula to standard

Given $a_n = -1.5a_{n-1}$, compare to $a_n = r \cdot a_{n-1}$.

Answer:

r = -1.5