Question

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 1

Answer: she received 21.875 hours of sleep during the 4 nights.

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=
`(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=(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.