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Sagot :
Explanation:
To find if the sequence is geometric we have to:
0. Divide each term by the previous term.
,1. Compare the quotients. If they are the same, a common ratio exists and the sequence is geometric.
a. 16, 4, 1, 1/4...
First we divide each term by the previous term:
[tex]\begin{gathered} \frac{4}{16}=\frac{1}{4} \\ \frac{1}{4}=\frac{1}{4} \\ \frac{\frac{1}{4}}{1}=\frac{1}{4} \end{gathered}[/tex]All these quotients are the same. This means that this sequence is geometric and its common ratio is 1/4
b. 3, -6, 12, -24...
Divide each term by the previous one:
[tex]\begin{gathered} \frac{-6}{3}=-2 \\ \frac{12}{-6}=-2 \\ \frac{-24}{12}=-2 \end{gathered}[/tex]All these quotients are equal. Therefore this sequence is geometric and its common ratio is -2
c. 8, 10, 12, 14...
Divide
[tex]\begin{gathered} \frac{10}{8}=\frac{5}{4} \\ \frac{12}{10}=\frac{6}{5} \\ \frac{14}{12}=\frac{7}{6} \end{gathered}[/tex]These quotients are all different. This is not a geometric sequence
Answers:
a. It is geometric. Common ratio = 1/4
b. It is geometric. Common ratio = -2
c. It is not geometric
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