Geometric Series problem -
Drake received 80 points on a project for school. He can make changes and receive one-tenth of the missing points back. He can do this 10 times. Create the formula for the sum of this geometric series, and explain your steps in solving for the maximum grade Drake can receive.

- chaotic_butterflies

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- chaotic_butterflies

@amistre64 if you're not busy could you possibly help me?

- amistre64

show me your idea ... and lets see if we can correct it

- amistre64

we may need to clarify this part: "He can make changes and receive one-tenth of the missing points back."
what does it mean to you?

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## More answers

- chaotic_butterflies

Does it mean that he can receive 1/10th of the 20 questions that he missed?

- chaotic_butterflies

Pardon my slow reply, my laptop keeps freezing >~<

- amistre64

it may mean, the 1/10 of the remaining points, after a submission.

- chaotic_butterflies

So wait, you mean like he'll be tested on the 20 that he missed and if he got them all right, then he would only receive a potion of that score to be added to his original score?
If that makes sense...

- amistre64

sounds like that to me.
but its pretty vague still
say he gets all of them correct in the submission, he gets an extra credit of 20(.1) = 2
but then what about any subsequent submission seeing how he got them all correct on the second try?

- amistre64

the grading scheme is rather senseless to me.
he can obtain more extra credit by getting things wrong and resubmitting? it doesnt seem to be a well thought out question to me.

- amistre64

Drake received 80 points on a project for school.
He can make changes and receive one-tenth of the missing points back.
make changes? say 1+1 = 3 and receive 1/10 of the missing
points back? How is this grading?

- chaotic_butterflies

That's the thing about virtual school, they focus so much on silly scenarios for their questions, and not enough time explaining the content in the lessons! I've tried to get help from the sources that have been offered to me, but it just doesn't seem to connect

- chaotic_butterflies

Oh hold on a minute I might have an idea

- amistre64

I have an idea too, but the question still makes no real sense
we can determine the number of points remaining after each submission, if .10 is used, we have .90 remaining
submission 0: 20
submission 1: 20 (.90)
submission 2: (20 (.90))(.90)
submission 3: (20 (.90)(.90))(.90)
...
right?

- chaotic_butterflies

I don't know if this has to do with anything but virtual school allows its students to retake tests if they need to, and they can reset it however many times until they have reached a certain amount of retakes. Each retake isn't influenced by the other... so if Drake is trying to get extra credit and he isn't satisfied with what he has, then he could reset and test himself on only the portion he got wrong - basically what all that rambling meant is that each retake probably doesn't influence another, I don't know if that's helpful or not it sounded better in my head

- chaotic_butterflies

What you said sounds more logical than what I just spewed out.

- amistre64

the thing is, it says he can make changes and receive .10 of the missing points back.
it does not say: "up to" .10
it does not say: "correct changes"
it does not say: anything at all to me

- amistre64

the remaining points after 10 submissions looks to be 20(.90)^(10)

- amistre64

but that isnt a series, its not a summation process that is being asked for.

- chaotic_butterflies

And this is why it's so important to have a physical math teacher for high school math, I used to actually know what on earth I was doing...

- amistre64

score0 = 80
score1 = 80 + 20(.10)
score2 = 80 + 20(.10) + 20(.90)(.10)
score3 = 80 + 20(.10) + 20(.90)(.10) + 20(.90)(.90)(.10)
this is what its looking at in my head ...

- amistre64

adding on 10% of the 90% thats left over from the previous submission

- amistre64

it actually gets us to the same amount as the sequence setup

- chaotic_butterflies

So should I go with that and assume the he gets the highest score on all of the tries to see what his maximun should be? I mean I guess I could do that but technically it's not creating a overall function

- chaotic_butterflies

Sequence setup?

- amistre64

its creating it, you just have to see it for what it is.
we an form a function from it

- amistre64

sequence is a list
series is a summation of the terms in a list.

- chaotic_butterflies

I understand that much, but I don't know what you're meaning

- amistre64

20(.90)^n gives us a list of values depending on n
20(.90)^10 = 6.97
which is the remaining points that cannot be claimed since its been submitted 10 times.

- amistre64

100 - 6.97 is the maximum score they can obtain.

- amistre64

the actual score process:
score1 = 80 + 20(.10)(.90)^0
score1 = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1
score2 = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+ 20(.10)(.90)^2
each score is a term, but part of it is also the summation of a geometric series.
score n = 80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+...+ 20(.10)(.90)^(n-1)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
this is a geometric series

- amistre64

do you know the formula for a geometric series?

- chaotic_butterflies

No Sir (or M'am)

- amistre64

then all this harder processing has been rather in vain dont you think ..

- amistre64

find the formula for the sum of a geometric series for me ..

- chaotic_butterflies

If you're asking me if I don't understand anything that you've shared with me, I've gotten the basic gist of it. I'll go look for that formula.

- amistre64

our initial score is 80, which means there is 20 points missing
we submit it and our score goes from 80,
to 80 + 20(.10),
and there is 20(.90) points left to plunder thru
we submit it again and our score goes from 80 + 20(.10),
to 80 + 20(.10) + 20(.90)(.10)
and there is 20(.90)(.90) points left to plunder thru
we submit it again and our score goes from 80 + 20(.10) + 20(.90)(.10)
to 80 + 20(.10) + 20(.90)(.10) + 20(.90)(.90)(.10)
and there is 20(.90)(.90)(.90) points left to plunder thru
etc etc etc

- chaotic_butterflies

I found yhe formula I think and it's terrifying

##### 1 Attachment

- amistre64

lol, that A formula, but thats the summation of an arithmetic series
we want:\[S=g_1\frac{1-r^n}{1-r}\]

- chaotic_butterflies

That's a little less scary but what do the letters stand for ?

- amistre64

g1 is a constant term, its a common factor among the setup
forget the 80, what is the common factor of the rest of it?

- chaotic_butterflies

1/10...?

- amistre64

80 + 20(.10)(.90)^0 + 20(.10)(.90)^1+...+ 20(.10)(.90)^(n-1)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
each term in the underlined part has 20(.10) in common, we can factor them out
80 + 20(.10) [(.90)^0 + (.90)^1+...+ (.90)^(n-1)]
^^^^^^^^^^^^^^^^^^^^^^^^^^
this is our series in terms of its ratio
g1 = 20(.10)
what is r?

- chaotic_butterflies

I've gotten to the point where I have to say the dreaded "I have no idea.."

- amistre64

hint: ratio starts with an 'r'
the setup in terms of our common ratio is:
(.90)^0 + (.90)^1+...+ (.90)^(n-1)
what is now common among this?

- chaotic_butterflies

(.90)

- amistre64

correct :)
so, g1 = 20(.10)
r = .90
what is n?

- amistre64

n = 1-, the number of submission we are allowed to make ...
\[score_{n}=80+g_1~\frac{1-r^n}{1-r}\]
\[score_{10}=80+20(.10)\frac{1-.90^{10}}{1-.90}\]
which is the same value as the more simpler route:
\[score_{10}=100-20(.90)^{10}\]

- amistre64

n=10

- amistre64

im going to run an errand now, so good luck, ask about what it is you are still concerned with.

- chaotic_butterflies

Alright, thank you very much!

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