Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.


1 , –5 , 25 , ...


Write your answer using decimals and integers.

an =
(
)n - 1

Answer 1

To find an equation that describes the sequence \(1, -5, 25, \ldots\), we first observe the terms:

1. **First term** (\(a_1\)): \(1\)
2. **Second term** (\(a_2\)): \(-5\)
3. **Third term** (\(a_3\)): \(25\)

Now let's identify the pattern and derive a formula.

Looking at the terms, it seems that each term could be related to powers of \(-5\):

- The first term (\(n = 1\)) is \(1 = (-5)^0\).
- The second term (\(n = 2\)) is \(-5 = (-5)^1\).
- The third term (\(n = 3\)) is \(25 = (-5)^2\).

Generally, we can express the \(n\)-th term as follows:

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

Thus, the equation that describes the sequence is:

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

This formula accurately produces the sequence defined by the terms you provided.