help please! sum of a geometric series!! word problem

Question

anonymous · Answer

Diana received 65 points on a project for school. She can make changes and receive three-tenths of the missing points back. She can make as many corrections as she wants. Create the formula for the sum of this geometric series and explain your steps in solving for the maximum grade Diana can receive. Identify this as converging or diverging.

kc_kennylau · Answer

Well I need to know the full mark or I wouldn't be able to know the missing points

anonymous · Answer

the full mark?

kc_kennylau · Answer

Is it 100?

anonymous · Answer

that  is all the problem, i believe the common ratio is 3/10 and the a1=65

anonymous · Answer

i dont know what you mean with full mark

kc_kennylau · Answer

Well the question is asking "three-tenth of the MISSING points"...

anonymous · Answer

dianna recived 65 points on the project so the missing points would be 35

kc_kennylau · Answer

a1 is indeed 65 but the common ratio wouldn't be 3/10

anonymous · Answer

it wouldn't?

kc_kennylau · Answer

Or else it would be "the new mark is three-tenths of the original mark"

kc_kennylau · Answer

Maybe write a recurring formula first? In order to know what's going on?

anonymous · Answer

i dont remember what the recrusive formula was, i belieb it was an = a1(r)^(n-1) ?

kc_kennylau · Answer

Not "the" recursive formula, "a" recursive formula

kc_kennylau · Answer

Recursive formula is expressing the next term in terms of the previous

kc_kennylau · Answer

So in this case the next term would be the previous plus three-tenths of the missing points

kc_kennylau · Answer

$$\Large a_{n+1}=a_n+\frac3{10}(100-a_n)$$

anonymous · Answer

yes i was typing that

kc_kennylau · Answer

Simplify this

anonymous · Answer

an+1 though?

anonymous · Answer

ok 1 sec

kc_kennylau · Answer

$\Large a_{n+1}$ is the next term while $\Large a_n$ is the original

anonymous · Answer

shouldnt you have to substitute 65 for n?

anonymous · Answer

or an int his case

kc_kennylau · Answer

No, 65 is $a_1$

kc_kennylau · Answer

So simplify it and we'd get:
$$\Large a_{n+1}=0.7a_n+30$$

kc_kennylau · Answer

So this isn't a geometric sequence at all

anonymous · Answer

no, it series

kc_kennylau · Answer

This isn't geometric at all

kc_kennylau · Answer

Geometric (series/sequence) wouldn't have +30 in the recursive formula

anonymous · Answer

ohhh I'm starting to think its arithmetic not geometric, geometric is what the word problem says it is, maybe with the equation 

$$65+\frac{ 3 }{ 10 }(2-1)$$

kc_kennylau · Answer

Arithmetic wouldn't have the multiplier 0.7

anonymous · Answer

equal to an or a2 in this case, since n=2

kc_kennylau · Answer

I'm wondering whether "missing points" really means the distance between the mark to the full mark

kc_kennylau · Answer

And what you wrote ain't a formula at all

anonymous · Answer

yes, missing points are 35, the distance between 65, her grade,  the full mark, which is 100

anonymous · Answer

to* the full mark

kc_kennylau · Answer

It's neither arithmetic nor geometric

kc_kennylau · Answer

The formula of a typical arithmetic sequence would be $\Large a_{n+1}=a_n+18$
The formula of a typical geometric sequence would be $\Large a_{n+1}=18a_n$

anonymous · Answer

maybe they want me to write a sigma notation?

kc_kennylau · Answer

So it's neither arithmetic nor geometric

anonymous · Answer

im guessing is not, i thought it was geometric series because the problem said so but now think is sigma notation what they want

anonymous · Answer

$$\sum_{n=1}^{\infty}$$

kc_kennylau · Answer

What I wrote was just the recursive formula, sigma notation requires the explicit formula

anonymous · Answer

i see

anonymous · Answer

maybe $$65 +\frac{ 3 }{ 10 }(n-1)$$

kc_kennylau · Answer

What's n?

kc_kennylau · Answer

So $a_2$ would be 65.3?

kc_kennylau · Answer

according to your formula?

anonymous · Answer

n is would be 2 in this case. we would get $$\sum_{n=1}^{\infty}\frac{ 3 }{ 10 }n -0.3$$
i believe

anonymous · Answer

yes

anonymous · Answer

the problem asks to create a formula, but i dont know if i am right or not

kc_kennylau · Answer

I have absolutely no idea how you got your formula

anonymous · Answer

the formula originates from an=a1+d(n-1)

kc_kennylau · Answer

So you already assumed that it's arithmetic

anonymous · Answer

yes arithmetic, but written in sigma notation, I'm not sure tho, i suck at word problems, theyre my weakness

kc_kennylau · Answer

It's not arithmetic at all

anonymous · Answer

then i dont know, im confuse

kc_kennylau · Answer

Oh man this question is trolling you

kc_kennylau · Answer

It's neither arithmetic nor geometric

anonymous · Answer

its a convergent sigma. but thanks for leaving man, appreciate the hard work.

anonymous · Answer

i believe the formula is $$sn = \frac{ a1 }{ 1-r }$$

anonymous · Answer

the formula im trying to get with this is

kc_kennylau · Answer

Man, this is the formula for a geometric series

kc_kennylau · Answer

The sequence in question is NEITHER arithmetic NOR geometric

the_fizicx99 · Answer

This is geometric.

anonymous · Answer

$$\sum_{i=1}^{\infty}a1(r)^{i-1}$$

anonymous · Answer

i knew! lol

anonymous · Answer

is my guess right or wrong...?

kc_kennylau · Answer

@tHe_FiZiCx99 How so?

anonymous · Answer

becaus 3/10 is being multiplied to the "missing" points and then being added to a1 which is 65, i believe thats why

kc_kennylau · Answer

If it involves the "missing" points it can't possibly be geometric...

the_fizicx99 · Answer

I'm going to try and make sense in this, I only have a few minutes left.

100 - 65 = 35

(assuming this is 100) she lost 35 points, she can get 3/10 of those points back

'35' is the missing point * $\ \dfrac{3}{10} $ = $\ \dfrac{35 * 3}{1 * 10} = \dfrac{105}{10} = 10.5 $ 65 + 10.5 = 75.5

anonymous · Answer

so if i were to write an equation for it would this be right?
$$\sum_{i=1}^{\infty}a1r ^{i-1} = \sum_{i=1}^{\infty}64(\frac{ 3 }{ 10 })^{i-1}$$

anonymous · Answer

65*

the_fizicx99 · Answer

a thought, it's converging at 75.5, the formula I would use is; s = 65 + 3/10*n

the_fizicx99 · Answer

Well, I have to get off it's midnight for me! Bye!

anonymous · Answer

same here:/

the_fizicx99 · Answer

Good luck :>

anonymous · Answer

come on mate, east coast:)? i need help, its a final test..

anonymous · Answer

its my last question before sleep

anonymous · Answer

well he was right about the 75.5, but i don't know how the equation would look

anonymous · Answer

@wio can you give us a hand mate?

anonymous · Answer

or want me to open a new question?

anonymous · Answer

The question is confusing.

anonymous · Answer

the questions quotes lesson 8.6 in my class, which is sigma notations. convergent and divergent. i know its geometric and i know its convergent because the ratio is 3/10

anonymous · Answer

So she starts with $a_1 = 100-64= 36$ missing points... and each time she can get $3/10$ths of them back?

anonymous · Answer

yes

anonymous · Answer

she has 65 and each time she gets 3/10ths  of 35(missing points) back

anonymous · Answer

a1=65
r=3/10
i believe this is right..?

anonymous · Answer

Wouldn't her highest score be if she doesn't miss anything on the first correction?

anonymous · Answer

Or does she get to correct the same question twice in a row?

anonymous · Answer

yes, the first time she missed something, and she got a 65/100, she is resubmitting to gain back 3/10ths of the missing points, 35

anonymous · Answer

she is able to resubmit as many times as she wants

anonymous · Answer

Well, if she submits infinite times then she will get back to 100.

anonymous · Answer

But I'm confused about what we are supposed to be expressing as a geometric series.

anonymous · Answer

i think we are supposed to be expressing as a convergent, sigma notation..?

anonymous · Answer

the problem is that it isn't an actual geometric series.