Answer:
Option b is correct.
The common ratio for the given geometric sequence is; ![\frac{-1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B2%7D)
Step-by-step explanation:
The given sequence is; -96, 48 , -24, 12 , -6, .....
Since, given sequence is Geometric
Geometric Sequence in which each term is found by multiplying the previous term by a constant(i.e common ratio)
In general we write geometric sequence as;
![a , ar, ar^2, ar^3 , .....](https://tex.z-dn.net/?f=a%20%2C%20ar%2C%20ar%5E2%2C%20ar%5E3%20%2C%20.....)
where a be the first term and r is the common ratio.
On comparing the given sequence with general geometric sequence;
we get
a = -96 ......[1]
ar = 48 ......[2]
ar^2 = -24 .....[3]
and so on....
To find the common ratio i.e, r;
Divide equation [2] by [1];
![\frac{ar}{a} =\frac{48}{-96}](https://tex.z-dn.net/?f=%5Cfrac%7Bar%7D%7Ba%7D%20%3D%5Cfrac%7B48%7D%7B-96%7D)
Simplify:
![r = \frac{-1}{2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
Similarly,
by dividing the equation [3] by [2] we get;
![\frac{ar^2}{ar} = \frac{-24}{48}](https://tex.z-dn.net/?f=%5Cfrac%7Bar%5E2%7D%7Bar%7D%20%3D%20%5Cfrac%7B-24%7D%7B48%7D)
Simplify:
![r = \frac{-1}{2}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
As, you can see that the value of r is constant i.e,
in the given sequence.
Therefore, the common ratio for the given geometric sequence is; ![r= \frac{-1}{2}](https://tex.z-dn.net/?f=r%3D%20%5Cfrac%7B-1%7D%7B2%7D)