Question

Which one of the following is a Geometric Sequence?

Answer 1

Letter d is s geometric sequence. You multiply or divide by the same number (r), common ratio to be a geometric sequence

Answer 2

Answer:

The geometric sequence among following is:

         Option: B

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

Step-by-step 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,

$-7\times \dfrac{-10}{7}=10$

but

$10\times \dfrac{-10}{7}\neq 23$

D)

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

Here

$2\times \dfrac{-3}{2}=-3$

$-3\times \dfrac{-3}{2}=\dfrac{9}{2}$

but

$\dfrac{9}{2}\times \dfrac{-3}{2}=\dfrac{-27}{4}\neq \dfrac{-18}{4}$

Hence, it is not a geometric sequence.