The sequence you provided is: 1, 2, 4, ...
This sequence can be identified as a geometric sequence where each term is multiplied by 2 to find the next term.
To write an equation for the \( n \)-th term of this sequence, we observe the following:
- The first term \( a_1 = 1 \) can be represented as \( 2^0 \).
- The second term \( a_2 = 2 \) can be represented as \( 2^1 \).
- The third term \( a_3 = 4 \) can be represented as \( 2^2 \).
From this observation, we can write the general formula for the \( n \)-th term (\( a_n \)) of the sequence:
\[ a_n = 2^{n-1} \]
Thus, the equation to describe the sequence is:
\[ a_n = 2^{n - 1} \]