which sequences are geometric? select three options.\n-2.7, -9, -30, -100, ...\n-1, 2.5, -6.25, 15.625…

Explanation:

Step1: Recall geometric - sequence formula

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

Step2: Check sequence - 1

For the sequence $-2.7,-9,-30,-100,\cdots$, $r_1=\frac{-9}{-2.7}=\frac{10}{3}$, $\frac{-30}{-9}=\frac{10}{3}$, $\frac{-100}{-30}=\frac{10}{3}$. It is a geometric sequence.

Step3: Check sequence - 2

For the sequence $-1,2.5,-6.25,15.625,\cdots$, $r_2=\frac{2.5}{-1}=-2.5$, $\frac{-6.25}{2.5}=-2.5$, $\frac{15.625}{-6.25}=-2.5$. It is a geometric sequence.

Step4: Check sequence - 3

For the sequence $9.1,9.2,9.3,9.4,\cdots$, $r_3=\frac{9.2}{9.1}\neq\frac{9.3}{9.2}$. It is not a geometric sequence.

Step5: Check sequence - 4

For the sequence $8,0.8,0.08,0.008,\cdots$, $r_4=\frac{0.8}{8}=0.1$, $\frac{0.08}{0.8}=0.1$, $\frac{0.008}{0.08}=0.1$. It is a geometric sequence.

Step6: Check sequence - 5

For the sequence $4, - 4,-12,-20,\cdots$, $r_5=\frac{-4}{4}=-1$, $\frac{-12}{-4}=3$. It is not a geometric sequence.

Answer:

-2.7, - 9, - 30, - 100, ...; -1, 2.5, - 6.25, 15.625, ...; 8, 0.8, 0.08, 0.008, ...