To find the equation for the sequence \( 12, 24, 48 \), we first observe the pattern in the terms.
- The first term is \( 12 \).
- The second term is \( 24 \), which is \( 12 \times 2 \).
- The third term is \( 48 \), which is \( 12 \times 4 \).
We can see that each term can be expressed in the form of a constant multiplied by powers of 2:
- The first term \( (n=1) \): \( 12 \times 2^{0} = 12 \)
- The second term \( (n=2) \): \( 12 \times 2^{1} = 24 \)
- The third term \( (n=3) \): \( 12 \times 2^{2} = 48 \)
Thus, we can summarize the pattern as follows:
\[ a_n = 12 \times 2^{n-1} \]
So, the equation to describe the sequence is:
\[ a_n = 12 \times (2)^{n-1} \]
This equation uses integers and shows how each term in the sequence can be generated.