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.