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

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= , where a= first term, r = common ratio, n= number of terms.

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

On simplifying we get

Sum =21.875 hours

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

55

step-by-step explanation: