The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$. We need to determine the type of sequence and find its general formula or any relevant information. It appears to be a geometric sequence.

1. Problem Description

The problem presents a sequence of numbers: $-6, -7.2, -8.64, -10.368, ...$. We need to determine the type of sequence and find its general formula or any relevant information. It appears to be a geometric sequence.

2. Solution Steps

Let's find the ratio between consecutive terms to determine if it is a geometric sequence.

$r_1 = \frac{-7.2}{-6} = 1.2$

$r_2 = \frac{-8.64}{-7.2} = 1.2$

$r_3 = \frac{-10.368}{-8.64} = 1.2$

Since the ratio between consecutive terms is constant ($1.2$), it is a geometric sequence.

The first term, $a_1$, is $-6$. The common ratio, $r$, is $1.2$.

The general formula for the $n$th term of a geometric sequence is:

$a_n = a_1 \cdot r^{n-1}$

Substituting the values, we get:

$a_n = -6 \cdot (1.2)^{n-1}$

3. Final Answer

The sequence is a geometric sequence with the general formula $a_n = -6 \cdot (1.2)^{n-1}$.