Question

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

( 1 , 1/2 , 1/6 , 1/24 , 1/120 , ... )

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

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

( 0 , 1 , 0 , -1 , 0 , ... )

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

( 1 , 3 , 5 , 7 , 9 , ... )

Answer 1

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

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

Explanation:

A geometric sequence has a common ratio in consecutive terms,

In sequence,

`1, (1)/(2), (1)/(6),(1)/(24),(1)/(120).....`

`(1/2)/(1)\\eq (1/6)/(1/2)\\eq (1/24)/(1/6)\\eq (1/120)/(1/24)...`

i.e.

`1, (1)/(2), (1)/(6),(1)/(24),(1)/(120).....` is not a Geometric sequence,

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

`(-2)/(1)\\eq (3)/(-2)\\eq (-4)/(3)\\eq (5)/(-4)...`

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

In sequence,

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

`(-2)/(1)=(4)/(-2)= (-8)/(4)= (16)/(-8)...`

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

In sequence,

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

`(1)/(0)\\eq (0)/(1)\\eq (-1)/(0)\\eq (0)/(-1)...`

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

In sequence,

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

`(3)/(9)=(1)/(3)= (1/3)/(1)= (1/9)/(1/3)...`

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

In sequence,

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

`(3)/(1)\\eq (5)/(3)\\eq (7)/(5)\\eq (9)/(7)...`

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