Question

Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.
-24, 48, -96
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

To find the equation that describes the sequence \(-24, 48, -96\), we can start by examining the first few terms:

1. \( a_1 = -24 \)
2. \( a_2 = 48 \)
3. \( a_3 = -96 \)

### Identifying the Pattern

Let's observe how each term relates to the position \( n \):

- The first term is \(-24\).
- The second term is \( 48\) which is \(-24(−2)\).
- The third term is \(-96\) which is \(48(−2)\) or \(-24(−4)\).

### Finding a Formula

There appears to be a pattern in the signs and the magnitudes. Each term seems to alternate signs and is multiplied by a factor related to \( (-2) \).

From this observation, we can conclude that with each term, the value is multiplied by \(-2\) raised to the power of \( n - 1\).

#### General Formula

The general formula for this sequence can be expressed as:

\[
a_n = -24 \cdot (-2)^{n-1}
\]

### Final Answer

Thus, the equation to describe the sequence is:

\[
a_n = -24(-2)^{n-1}
\]