Question

Write an equation to describe the sequence below.Use n to represent the position of a term in the sequence,where n = 1 for the first term.
3.77, 15.08, 60.32
Write your answer using decimals and integers.
an = __ (__)n-1

Answer 1

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:

\[
a_n = 3.77 \cdot 4^{(n-1)}
\]