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.
-2, 4, -8
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

To describe the sequence \(-2, 4, -8\), we first observe the pattern of the terms.

1. The first term (when \(n = 1\)) is \(-2\).
2. The second term (when \(n = 2\)) is \(4\).
3. The third term (when \(n = 3\)) is \(-8\).

Next, let's examine the pattern in the terms:

- The first term is \(-2\) (which is \(-2 \times 1\)).
- The second term is \(4\) (which is \(-2 \times -2\)).
- The third term is \(-8\) (which is \(-2 \times 4\)).

There is a clear trend where each term alternates in sign, and each term can be represented by multiplying the previous term by \(-2\).

We can express the \(n\)-th term of the sequence as:
\[
a_n = -2 \times (-2)^{n-1}
\]
Thus, putting it in the desired format:
\[
a_n = -2 \cdot (-2)^{n-1}
\]

So, the completed equation to describe the sequence is:
\[
a_n = -2 \cdot (-2)^{n-1}
\]