Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


8 , –40 , 200 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find the equation that describes the sequence \( 8, -40, 200, \ldots \), we need to identify a pattern in the terms.

1. **Finding the pattern**: Let's look at the given terms individually:
- **First term** (\(a_1\)): 8
- **Second term** (\(a_2\)): -40
- **Third term** (\(a_3\)): 200

2. **Finding the ratios**:
- From \(8\) to \(-40\): \(-40 / 8 = -5\)
- From \(-40\) to \(200\): \(200 / -40 = -5\)

The ratio of each term to its previous term seems to be \(-5\), so it suggests that each term is being multiplied by \(-5\).

3. **Expressing the general term**:
- The first term is \(a_1 = 8\).
- Each subsequent term can be calculated as:
\[
a_n = a_{n-1} \cdot (-5)
\]
- Therefore, you can express this using the first term:
\[
a_n = 8 \cdot (-5)^{n-1}
\]

Putting it all together, the equation that describes the nth term of the sequence is:

\[
a_n = 8 \cdot (-5)^{n-1}
\]

This represents the sequence you provided.