Respuesta :
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,
[tex]1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....[/tex]
[tex]\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...[/tex]
i.e.
[tex]1, \frac{1}{2}, \frac{1}{6},\frac{1}{24},\frac{1}{120}.....[/tex] is not a Geometric sequence,
1 , -2 , 3 , -4 , 5 , ...
[tex]\frac{-2}{1}\neq \frac{3}{-2}\neq \frac{-4}{3}\neq \frac{5}{-4}...[/tex]
i.e. 1 , -2 , 3 , -4 , 5 , ... is not a Geometric sequence,
In sequence,
1 , -2 , 4 , -8 , 16 , ...
[tex]\frac{-2}{1}=\frac{4}{-2}= \frac{-8}{4}= \frac{16}{-8}...[/tex]
i.e. 1 , -2 , 4 , -8 , 16 , .... is a Geometric sequence,
In sequence,
0 , 1 , 0 , -1 , 0 , .....
[tex]\frac{1}{0}\neq \frac{0}{1}\neq \frac{-1}{0}\neq \frac{0}{-1}...[/tex]
i.e. 0 , 1 , 0 , -1 , 0 , .....is not a Geometric sequence,
In sequence,
9 , 3 , 1 , 1/3 , 1/9 , ...
[tex]\frac{3}{9}=\frac{1}{3}= \frac{1/3}{1}= \frac{1/9}{1/3}...[/tex]
i.e. 9 , 3 , 1 , 1/3 , 1/9 , ... is a Geometric sequence,
In sequence,
1 , 3 , 5 , 7 , 9 , ...
[tex]\frac{3}{1}\neq \frac{5}{3}\neq \frac{7}{5}\neq \frac{9}{7}...[/tex]
i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence
