Question

select all of the geometric sequences.
time
(days)number
of cells
13
26
39
412
2,4,8,16...
2,4,6,8...
time
(days)number
of cells

Explanation:

Step1: Recall the definition of a geometric sequence

A geometric sequence has a common ratio \(r\), where \(r=\frac{a_{n + 1}}{a_{n}}\) for \(n\geq1\).

Step2: Analyze the first table

For the table with time and number of cells:
\(r_1=\frac{6}{3}=2\), \(r_2=\frac{9}{6}=1.5\), \(r_3=\frac{12}{9}=\frac{4}{3}\). Since the ratios are not equal, it is not a geometric sequence.

Step3: Analyze the sequence \(2,4,8,16,\cdots\)

\(r=\frac{4}{2} = 2\), \(\frac{8}{4}=2\), \(\frac{16}{8}=2\). The common ratio \(r = 2\), so it is a geometric sequence.

Step4: Analyze the sequence \(2,4,6,8,\cdots\)

\(r_1=\frac{4}{2}=2\), \(r_2=\frac{6}{4}=1.5\), \(r_3=\frac{8}{6}=\frac{4}{3}\). Since the ratios are not equal, it is not a geometric sequence.

Answer:

The geometric sequence is \(2,4,8,16,\cdots\)