Mathematics: Rosalie sleeps 8 hours the first night of finals week. Each night after, she stays up later to study and sleeps 75% as much as she did the previous night. How many total hours of sleep does she receive during the 4 nights of finals week? Do this without finding each night and adding for a total

answer: Step-by-step explanation:...

Rosalie sleeps 8 hours the first night of finals week.

phaalexander

09.07.2021

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= $\dfrac{a(r^n-1)}{r-1}$ , where a= first term, r = common ratio, n= number of terms.

Put a= 8, r=0.75 and n =4, we get

$Sum=\dfrac{8((0.75)^4-1)}{0.75-1}$

On simplifying we get

Sum =21.875 hours

Hence, she received 21.875 hours of sleep during the 4 nights.

0,0(0 оценок)