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

1 answer

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:

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