Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


8 , 24 , 72 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find the equation that describes the given sequence \(8, 24, 72, \ldots\), we can begin by examining the pattern in the sequence.

1. **Identify the ratio between terms:**
- \( \frac{24}{8} = 3 \)
- \( \frac{72}{24} = 3 \)

This indicates that each term is multiplied by 3 to get the next term.

2. **Express the terms:**
- The first term \(a_1 = 8\)
- The second term \(a_2 = 8 \times 3 = 24\)
- The third term \(a_3 = 8 \times 3^2 = 72\)

Since each term can be expressed as an initial term multiplied by \(3\) raised to a power, we can express the \(n\)-th term of the sequence as follows:

\[
a_n = 8 \times 3^{n-1}
\]

Thus, the equation for the \(n\)-th term in the sequence is:

\[
a_n = 8 \times 3^{n-1}
\]