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}.....](https://tex.z-dn.net/?f=1%2C%20%5Cfrac%7B1%7D%7B2%7D%2C%20%5Cfrac%7B1%7D%7B6%7D%2C%5Cfrac%7B1%7D%7B24%7D%2C%5Cfrac%7B1%7D%7B120%7D.....)
![\frac{1/2}{1}\neq \frac{1/6}{1/2}\neq \frac{1/24}{1/6}\neq \frac{1/120}{1/24}...](https://tex.z-dn.net/?f=%5Cfrac%7B1%2F2%7D%7B1%7D%5Cneq%20%5Cfrac%7B1%2F6%7D%7B1%2F2%7D%5Cneq%20%5Cfrac%7B1%2F24%7D%7B1%2F6%7D%5Cneq%20%5Cfrac%7B1%2F120%7D%7B1%2F24%7D...)
i.e.
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}...](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B1%7D%5Cneq%20%5Cfrac%7B3%7D%7B-2%7D%5Cneq%20%5Cfrac%7B-4%7D%7B3%7D%5Cneq%20%5Cfrac%7B5%7D%7B-4%7D...)
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}...](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B1%7D%3D%5Cfrac%7B4%7D%7B-2%7D%3D%20%5Cfrac%7B-8%7D%7B4%7D%3D%20%5Cfrac%7B16%7D%7B-8%7D...)
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}...](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B0%7D%5Cneq%20%5Cfrac%7B0%7D%7B1%7D%5Cneq%20%5Cfrac%7B-1%7D%7B0%7D%5Cneq%20%5Cfrac%7B0%7D%7B-1%7D...)
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}...](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B9%7D%3D%5Cfrac%7B1%7D%7B3%7D%3D%20%5Cfrac%7B1%2F3%7D%7B1%7D%3D%20%5Cfrac%7B1%2F9%7D%7B1%2F3%7D...)
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}...](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B1%7D%5Cneq%20%5Cfrac%7B5%7D%7B3%7D%5Cneq%20%5Cfrac%7B7%7D%7B5%7D%5Cneq%20%5Cfrac%7B9%7D%7B7%7D...)
i.e. 1 , 3 , 5 , 7 , 9 , ... is not a Geometric sequence