Question

Which one of the following is a Geometric Sequence?

Answer 1

The geometric sequence among following is:

Option: B

8 , 4 , 2 , 1 , 1/2 , 1/4 ,.....

Explanation:

Geometric sequence--

A sequence is said to be a geometric sequence if each of the number in the sequence is a constant multiple of the preceding term in the sequence.

This constant multiple is known as the common ratio (r)

i.e. the sequence is given by:

a,ar,ar²,ar³,.....

A)

0,1,2,3,......

It is a arithmetic sequence and not a geometric sequence .

Since, each of the term is increasing by 1 as compared to the preceding term of the sequence.

B)

8,4,2,1,1/2,1/4,.....

It is a geometric sequence.

Since, each term of the sequence is a constant multiple of 1/2 of the preceding term of the sequence.

i.e. 8×(1/2)=4

4×(1/2)=2

2×(1/2)=1

1×(1/2)=1/2

and so on.

i.e. the common ratio is: 1/2

C)

-7,10,23,36,.....

This is not a geometric sequence.

Since,

`-7* (-10)/(7)=10`

but

`10* (-10)/(7)\\eq 23`

D)

2,-3,9/2,-18/4

Here

`2* (-3)/(2)=-3`

`-3* (-3)/(2)=(9)/(2)`

but

`(9)/(2)* (-3)/(2)=(-27)/(4)\\eq (-18)/(4)`

Hence, it is not a geometric sequence.