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
\(10\times \dfrac{-10}{7}
eq 23\)
D)
2,-3,9/2,-18/4
Here
\(2\times \dfrac{-3}{2}=-3\)
\(-3\times \dfrac{-3}{2}=\dfrac{9}{2}\)
but
\(\dfrac{9}{2}\times \dfrac{-3}{2}=\dfrac{-27}{4}
eq \dfrac{-18}{4}\)
Hence, it is not a geometric sequence.
