Question

Writeanequationtodescribethesequencebelow.Usentorepresentthepositionofaterminthesequence,wheren = 1forthefirstterm.
1 , 3 , 9 , ...
Write your answer using decimals and integers
.
an = _(_)^ n^ -^ 1

Answer 1

To find an equation that describes the sequence \(1, 3, 9, \ldots\), let's analyze the pattern.

Looking at the terms:
- The 1st term \(a_1 = 1\)
- The 2nd term \(a_2 = 3\)
- The 3rd term \(a_3 = 9\)

We can see that the terms can be expressed as powers of 3:

- \(1 = 3^0\)
- \(3 = 3^1\)
- \(9 = 3^2\)

From this pattern, we can see that the \(n\)-th term of the sequence is given by the formula \(a_n = 3^{n-1}\).

So, filling in the blanks in your equation, we have:

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

This function correctly represents the sequence as you requested.