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cluponka [151]
2 years ago
13

Which of the following are examples of a geometric sequence? Select any and all that apply: may be more than one correct answer.

Mathematics
1 answer:
nevsk [136]2 years ago
4 0

Answer:

( 1 , -2 , 4 , -8 , 16 , ... )

( 9 , 3 , 1 , 1/3 , 1/9 , ... )

Step-by-step explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....

\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...

i.e.

1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}..... is not a Geometric sequence,

1 , -2 , 3 , -4 , 5 , ...

\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...

i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,

In sequence,

1 , -2 , 4 , -8 , 16 , ...

\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...

i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,

In sequence,

0 , 1 , 0 , -1 , 0 , .....

\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...

i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,

In sequence,

9 , 3 , 1 , 1/3 , 1/9 , ...

\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...

i.e.  9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,

In sequence,

1 , 3 , 5 , 7 , 9 , ...

\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...

i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence

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