Answer: she received 21.875 hours of sleep during the 4 nights.
Step-by-step explanation:
Rosalie is following a geometric sequence(GP) by having a common rate of sleep .
as 75% or 0.75%.
Formula for a sum in GP= [tex]\dfrac{a(r^n-1)}{r-1}[/tex], where a= first term, r = common ratio, n= number of terms.
Put a= 8, r=0.75 and n =4, we get
[tex]Sum=\dfrac{8((0.75)^4-1)}{0.75-1}[/tex]
On simplifying we get
Sum =21.875 hours
Hence, she received 21.875 hours of sleep during the 4 nights.
