2. what is the common ratio in this recursive definition?
$a_1 = 4$
$a_n = -1.5a_{n-1}$

$\bigcirc$ $r = 1.5$
$\bigcirc$ $a_{n-1}$?
$\bigcirc$ $r = -1.5$
$\bigcirc$ $r = 4$

Question

2. what is the common ratio in this recursive definition?
$a_1 = 4$
$a_n = -1.5a_{n-1}$

$\bigcirc$ $r = 1.5$
$\bigcirc$ $a_{n-1}$?
$\bigcirc$ $r = -1.5$
$\bigcirc$ $r = 4$

Accepted Answer

# Explanation:

⚡ Using what you learned: Recursive and Explicit Formulas

## Step 1: Identify the recursive formula structure

The given recursive definition is:
$$
\begin{aligned}
a_1 &= 4 \
a_n &= -1.5 a_{n-1}
\end{aligned}
$$

A recursive formula for a geometric sequence has the general form:
$$
a_n = r \cdot a_{n-1}
$$
where $ r $ represents the common ratio.

## Step 2: Determine the value of $ r $

By comparing the given formula to the general form:
$$
a_n = -1.5 a_{n-1}
$$
The multiplier is:
$$
r = -1.5
$$

# Answer:

$ r = -1.5 $

Sovi.AI - AI Math Tutor