Answer:
LAST OPTION: 
Step-by-step explanation:
For this exercise it is important to remember the Power of a power property, which states that:
The expression given in the exercise is:
Therefore, in order to simplify it, you must apply the Power of a power property explained before.
Then, you get the following expression:
As you can notice, the expression obtained matches with the expression provided in the last option.
The nth term of the geometric sequence is:
an=ar^(n-1)
where
a=first term
r=common ratio
n=nth term
from the question:
120=ar(3-1)
120=ar^2
a=120/(r^2)....i
also:
76.8=ar^(5-1)
76.8=ar^4
a=76.8/r^4.....i
thus from i and ii
120/r^2=76.8/r^4
from above we can have:
120=76.8/r²
120r²=76.8
r²=76.8/120
r²=0.64
r=√0.64
r=0.8
hence:
a=120/(0.64)=187.5
therefore the formula for the series will be:
an=187.5r^0.8
First get all the terms on the same side:
Now solve using the quadratic formula which is:
Plug in the values:
So the answer is:
