Phillip received 75 points on a project for school. He can make changes and receive two-tenths of the missing points back. He can make corrections as many times as he wants. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Phillip can receive. Identify this as converging or diverging.

Question

rocklionmba · Answer

anyone can help? im lost

greencat · Answer

Could you explain "He can make corrections as many times as he wants."

rocklionmba · Answer

he can do it infinitely.

greencat · Answer

But how does that contribute to the geometric series.

rocklionmba · Answer

oh...that means... im not sure my brain is scattered right now im help 2 other people

rocklionmba · Answer

anybody?

rocklionmba · Answer

@bohotness

rocklionmba · Answer

@iambatman

bohotness · Answer

brb

rocklionmba · Answer

ok

rocklionmba · Answer

can you help @Chunkymonkay

rocklionmba · Answer

hello?

rocklionmba · Answer

@Nnesha @wio

rocklionmba · Answer

ive been stuck on this for over an hour

rocklionmba · Answer

are you there?

rocklionmba · Answer

@bibby

jim_thompson5910 · Answer

It might help to write out the first few terms of the geometric sequence

rocklionmba · Answer

how? Im sorry im usually better at math but FLVS seems to hate me

jim_thompson5910 · Answer

The first term is 25 (assuming 100 is a perfect score, 100-75 = 25)

the second term is 25*(2/10) = 50/10 = 5

the third term is 5*(2/10) = 10/10 = 1

notice how I'm multiplying each term by 2/10 to get the next term. Using this idea, what is the fourth term?

rocklionmba · Answer

.2

jim_thompson5910 · Answer

or 2/10 = 1/5, yes

jim_thompson5910 · Answer

you repeat this over and over to generate the terms of the sequence

jim_thompson5910 · Answer

once you have your terms, you add them all up to get the sum of the geometric series

rocklionmba · Answer

but this is a infinite series

jim_thompson5910 · Answer

because we have infinitely many terms, this means that it's impossible to generate every term and add them up

so we must take a shortcut and use a formula

jim_thompson5910 · Answer

in this case,

a = 25 is the first term
r = 2/10 = 1/5 = 0.2 is the common ratio

rocklionmba · Answer

I think I know it

jim_thompson5910 · Answer

since |r| < 1 is true, which formula will apply here?

jim_thompson5910 · Answer

oh wait, I'm realizing that 25 isn't the first term. If it was, then he'd get all his points back by adding on that first term lol

so ignore that

the first term is actually 25*(2/10) = 5

jim_thompson5910 · Answer

first term: a = 5
common ratio: r = 0.2

rocklionmba · Answer

attachment

jim_thompson5910 · Answer

that's if you are adding up n terms

jim_thompson5910 · Answer

where n is a finite number

jim_thompson5910 · Answer

but we're adding up an infinite number of terms

rocklionmba · Answer

ooohhh then idk

jim_thompson5910 · Answer

the formula is 

S = a/(1-r)

jim_thompson5910 · Answer

'a' is the first term
r is the common ratio
S is the sum of the infinite geometric series


the condition is that |r| < 1 must be true

jim_thompson5910 · Answer

since r = 0.2 and |0.2| < 1 is true, the condition |r| < 1 is true

rocklionmba · Answer

that also makes it convergent

jim_thompson5910 · Answer

yes, if |r| < 1 wasn't true, then it wouldn't converge. It would go off to infinity

rocklionmba · Answer

that's divergent

jim_thompson5910 · Answer

if it doesn't converge, then it diverges, yes

in this case, this geometric series converges to a fixed number S

rocklionmba · Answer

so we do 75/(1-(2/10 or .2))

jim_thompson5910 · Answer

the first term is actually 5

jim_thompson5910 · Answer

I made a correction (it's not 25, it's actually 5)

jim_thompson5910 · Answer

you multiply 25 by 0.2 to get 5

rocklionmba · Answer

wait why are we multiply 25*.2 or is that an example

jim_thompson5910 · Answer

the score is 75 out of 100

the missing points is 25

jim_thompson5910 · Answer

"He can make changes and receive two-tenths of the missing points back"

so the first change he makes (assuming it's correct) gets him back 5 points because 2/10ths of 25 is 5

jim_thompson5910 · Answer

ie, the first correct change brings him 5 points back

this is why 5 is the first term

jim_thompson5910 · Answer

the next change brings him back 5*(0.2) = 1 point back

rocklionmba · Answer

then you do 5 then as the first term witch makes you get 1, and that would be your first term again

jim_thompson5910 · Answer

no, you would only have 1 first term

jim_thompson5910 · Answer

it's the amount of points brought back with that first change

jim_thompson5910 · Answer

or first correction

rocklionmba · Answer

ok

jim_thompson5910 · Answer

so,

a = 5
r = 0.2

rocklionmba · Answer

5/(1-.2)

jim_thompson5910 · Answer

yes

rocklionmba · Answer

that's 6.25

jim_thompson5910 · Answer

correct, that is the infinite sum

jim_thompson5910 · Answer

As an exercise, I recommend you generate a bunch of terms (say 5 or 6) and add them up. You should notice that the sum you get is close to 6.25. The more terms you generate, the closer that sum gets to 6.25

jim_thompson5910 · Answer

That means the highest score he can get is 75+6.25 = 81.25