The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$ and asks us to identify the pattern and determine the type of sequence. It's likely a geometric or arithmetic sequence, but we should confirm.

1. Problem Description

The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$ and asks us to identify the pattern and determine the type of sequence. It's likely a geometric or arithmetic sequence, but we should confirm.

2. Solution Steps

First, check if it is an arithmetic sequence by calculating the differences between consecutive terms:

$-7.2 - (-6) = -1.2$

$-8.64 - (-7.2) = -1.44$

$-10.368 - (-8.64) = -1.728$

Since the differences are not constant, this is not an arithmetic sequence.

Next, check if it is a geometric sequence by calculating the ratios between consecutive terms:

$\frac{-7.2}{-6} = 1.2$

$\frac{-8.64}{-7.2} = 1.2$

$\frac{-10.368}{-8.64} = 1.2$

Since the ratios are constant, this is a geometric sequence with a common ratio $r = 1.2$. The first term is $a_1 = -6$.

The formula for the nth term of a geometric sequence is

$a_n = a_1 * r^{n-1}$

In this problem, we are asked to determine the type of sequence, and possibly find the next term, but not explicitly specified.

3. Final Answer

The sequence is a geometric sequence with a common ratio of $1.2$.