last semester i got GPA=3 ,if the GPA for the next semester is always the average of the previous one.Suppose i get GPA=4 for the next 8 semesters,is it possible to end up with average GPA=4,when i graduate

Question

last semester i got GPA=3 ,if the GPA for the next semester is always the average of the previous one.Suppose  i get GPA=4 for the next 8 semesters,is it possible to end up with average GPA=4,when i graduate

anonymous · Answer

GPA =grade point average

primeralph · Answer

No. To get a 4.0 exactly, you need a 4.0 all through.

primeralph · Answer

Infinitely, yes due to finite precision.
In 8 semesters, no.

anonymous · Answer

okay thanx thi problem is original ,not from any book i was struggling with it

primeralph · Answer

You're welcome.

anonymous · Answer

$$\huge GPA=\frac{\frac{\frac{ x+4}{2}+4}{2}+4}{2}...$$
suppose i have many years to study what is the minimum semesters i need to get GPA=4 if my current GPA=3.9

primeralph · Answer

Depends on precision (number of decimal places).
You can never get there if your school uses as many decimal places as possible.

anonymous · Answer

interesting, thanks @primeralph

primeralph · Answer

@Jonask  If they use 2 decimal places like most schools, then yes you can get there.

anonymous · Answer

ooh okay but the best way to get it is still 4,my school uses 2 dp

primeralph · Answer

The best way is 4. If you have a 3.9, you can still get it, but you'll need to work hard.

whpalmer4 · Answer

Your GPA isn't computed by averaging your current GPA with the next grading period's GPA, it is computed by summing the grades over all of the grading periods and then dividing by the number of periods...so the continued fraction you wrote isn't applicable.