To find an equation for the sequence \(3.77, 15.08, 60.32\), we first examine how the sequence progresses.
Let's denote the terms of the sequence as follows:
- \(a_1 = 3.77\)
- \(a_2 = 15.08\)
- \(a_3 = 60.32\)
Next, we calculate the ratios of consecutive terms to see if there’s a common multiplier:
\[ \frac{a_2}{a_1} = \frac{15.08}{3.77} \approx 4 \] \[ \frac{a_3}{a_2} = \frac{60.32}{15.08} \approx 4 \]
It appears that each term is approximately 4 times the previous term. Thus, we can express the \(n\)th term in terms of the first term multiplied by a factor of 4 raised to the power of \(n-1\):
\[ a_n = a_1 \cdot 4^{(n-1)} \]
Substituting \(a_1 = 3.77\):
\[ a_n = 3.77 \cdot 4^{(n-1)} \]
So, the equation describing the sequence is:
\[ a_n = 3.77 \cdot 4^{(n-1)} \]