Question

1. time (in days) 1 2 3 4 number of cells 5 8 12.8 20.48 a. arithmetic or geometric? b. recursive: c. explicit:

Explanation:

Step1: Check for arithmetic sequence

Find the differences between consecutive terms. \(12.8 - 8=4.8\), \(20.48 - 12.8 = 7.68\). Since the differences \(4.8\) and \(7.68\) are not equal, it is not an arithmetic sequence.

Step2: Check for geometric sequence

Find the ratios between consecutive terms. \(\frac{12.8}{8}=1.6\), \(\frac{20.48}{12.8}=1.6\). Since the ratio between consecutive terms is constant (\(r = 1.6\)), it is a geometric sequence.

Step3: Write the recursive formula for a geometric sequence

The general form of a recursive formula for a geometric sequence is \(a_n=a_{n - 1}\times r\), where \(a_1\) is the first - term and \(r\) is the common ratio. Here \(a_1 = 5\) and \(r = 1.6\), so \(a_n=a_{n - 1}\times1.6,a_1 = 5\).

Step4: Write the explicit formula for a geometric sequence

The general form of an explicit formula for a geometric sequence is \(a_n=a_1\times r^{n - 1}\). Substituting \(a_1 = 5\) and \(r = 1.6\), we get \(a_n=5\times(1.6)^{n - 1}\).

Answer:

a. Geometric
b. \(a_n=a_{n - 1}\times1.6,a_1 = 5\)
c. \(a_n=5\times(1.6)^{n - 1}\)