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.
-28, -84, -252,
Write your answer using decimals and integers.
an = __ ( __ )^n-1

Answer 1

To find the equation for the given sequence \(-28, -84, -252\), we first need to determine whether it's an arithmetic or geometric sequence.

1. **Identify the Sequence Type**:
- **Common Ratio**: Let's see if this sequence is geometric by calculating the ratio between terms.
\[
\frac{-84}{-28} = 3
\]
\[
\frac{-252}{-84} = 3
\]
Since the ratio between consecutive terms is consistent (both are 3), this is a geometric sequence.

2. **General Form of a Geometric Sequence**:
The general form of a geometric sequence can be expressed as:
\[
a_n = a_1 \cdot r^{(n-1)}
\]
where \(a_1\) is the first term and \(r\) is the common ratio.

3. **Identify the Constants**:
- The first term \(a_1 = -28\)
- The common ratio \(r = 3\)

4. **Write the Equation**:
Now we can substitute these values into the equation:
\[
a_n = -28 \cdot (3)^{(n-1)}
\]

Thus, the equation for the sequence is:
\[
\boxed{a_n = -28 \cdot (3)^{(n-1)}}
\]