Calculating row geometric sequence | Mathematics | Page 1

fierce bluffBOT Mar 13, 2024, 1:29 PM

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civic sparrow Mar 13, 2024, 1:32 PM

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what answer does the answerbook give

halcyon flume Mar 13, 2024, 1:32 PM

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The answerbook says \frac{111111}{200000}

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111111/200000

civic sparrow Mar 13, 2024, 1:33 PM

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you forgot to simplify your fraction answer

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when you simplify a fraction, both the numerator and the denominator change

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also how did you get 99990/180000

halcyon flume Mar 13, 2024, 1:34 PM

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Ill show my calculation 1 sec pls

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Probably some really stupid mistake 😦

civic sparrow Mar 13, 2024, 1:36 PM

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Ive made worse

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if youre ever not sure, you can use a calculator to verify each step

halcyon flume Mar 13, 2024, 1:37 PM

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xD, i'm a king when it comes to stupid mistakes.

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*champion

halcyon flume Mar 13, 2024, 1:38 PM

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civic sparrow if youre ever not sure, you can use a calculator to verify each step

true, but honestly I used the same strategy and formula. So it should be right.

civic sparrow Mar 13, 2024, 1:38 PM

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what you did here isnt correct

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you need to know where the +1 in the n+1 comes from

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the steps you are currently doing use a different version fo the formula that does not have a +1

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so your formula is $\text{first term}\cdot\frac{1-(\text{ratio})^5}{1-\text{ratio}}$

brittle lichenBOT Mar 13, 2024, 1:40 PM

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mtt07734

halcyon flume Mar 13, 2024, 1:40 PM

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What does ratio mean, i'm sorry

civic sparrow Mar 13, 2024, 1:40 PM

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1/10

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you used the capital letter R for it, remember

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it stands for Ratio

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(also you need to use a lowercase r not a capital one)

halcyon flume Mar 13, 2024, 1:40 PM

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Ah okay thanks

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I'm gonna recalculate it

civic sparrow Mar 13, 2024, 1:41 PM

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ok

halcyon flume Mar 13, 2024, 1:41 PM

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But now you say first term *

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But the formula should stay the same, shouldn't it?

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Because

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Hold on: you most likely know, but ill show you the only formula i've gotten from the theory book to solve these. Ill send a picture

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This is the formula I've used and the only one for these problems I've got from the theory book. It should be solveable with this formula.

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A0 = begin term so 5/10
R = 1/10 (I assume)
An= 5/1.000.000

civic sparrow Mar 13, 2024, 2:05 PM

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halcyon flume

you calculated N wrong

halcyon flume Mar 13, 2024, 2:06 PM

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Like in the formula or in general?

civic sparrow Mar 13, 2024, 2:06 PM

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in this particular formula

halcyon flume Mar 13, 2024, 2:06 PM

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n + 1

-5 + 1

civic sparrow Mar 13, 2024, 2:07 PM

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and that answers?

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do you know what the N means?

halcyon flume Mar 13, 2024, 2:10 PM

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civic sparrow do you know what the N means?

Not really, sorry

halcyon flume Mar 13, 2024, 2:10 PM

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civic sparrow and that answers?

-4?

civic sparrow Mar 13, 2024, 2:12 PM

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halcyon flume -4?

no

civic sparrow Mar 13, 2024, 2:12 PM

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halcyon flume Not really, sorry

there are three definitions for N depending on how you view the series and the formula you use

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first, do you know the notation for how to write a sequence down

halcyon flume Mar 13, 2024, 2:13 PM

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Sigma notation?

civic sparrow Mar 13, 2024, 2:13 PM

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do you know the notation for how to write a sequence down

halcyon flume Mar 13, 2024, 2:14 PM

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Then, I don't think so.

civic sparrow Mar 13, 2024, 2:14 PM

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do you remember a0, a1, a2 meaning anything?

halcyon flume Mar 13, 2024, 2:14 PM

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Ah yes, I know it

civic sparrow Mar 13, 2024, 2:14 PM

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you know a0, a1, a2 is called a "sequence"?

halcyon flume Mar 13, 2024, 2:15 PM

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Yes

civic sparrow Mar 13, 2024, 2:15 PM

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then do you know the notation for how to write a sequence down

halcyon flume Mar 13, 2024, 2:15 PM

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a1 = a0 * r = a0r

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Do you mean that?

civic sparrow Mar 13, 2024, 2:15 PM

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now do you know what the n in an meant?

halcyon flume Mar 13, 2024, 2:15 PM

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aN = aN-1 * r

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Honestly, no

civic sparrow Mar 13, 2024, 2:16 PM

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its a variable

halcyon flume Mar 13, 2024, 2:16 PM

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like aN is the end term

civic sparrow Mar 13, 2024, 2:16 PM

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no its not

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n is just a regular variable thats commonly used for indices

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(indices is index but plural)

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(the number in the lower-right of a is called an "index")

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so n fundamentally does not have any meaning tied to it

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part of the problem is what you begin the sequence with

halcyon flume Mar 13, 2024, 2:17 PM

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civic sparrow so n fundamentally does not have any meaning tied to it

Ah yes it defines on which position it is, right?

civic sparrow Mar 13, 2024, 2:17 PM

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sure

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part of the problem is what you begin the sequence with
you can either choose the index to begin at 0 or at 1

halcyon flume Mar 13, 2024, 2:17 PM

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Begin at 0

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Beginning at 0

civic sparrow Mar 13, 2024, 2:18 PM

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then the sequence begins at a0 and then goes a1, a2, a3 ...

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to represent an arbitrary term at index n, you use an

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n is not a special letter for this purpose

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if you want to use the letter k for the index, you use ak

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the letter i for the index is common as well

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so n here is already very broad

halcyon flume Mar 13, 2024, 2:19 PM

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civic sparrow the letter i for the index is common as well

Yes thanks, I know. I have done that before with A and B because Ak index was not equal to 0

civic sparrow Mar 13, 2024, 2:19 PM

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no idea what you mean by that

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the index can either begin at 0 or 1 regardless of what letter youre using

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its a separate, independent choice

halcyon flume Mar 13, 2024, 2:20 PM

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I changed variables with arithmetic sequences before

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So when Ak= not equal to 1 I had to change variables

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So I did B = K + ( number to make it 1)

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So if Ak was -2 than It would be B = K + 3

civic sparrow Mar 13, 2024, 2:21 PM

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thats not a green flag

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not a red one either

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we can address what youre doing wrong there later

halcyon flume Mar 13, 2024, 2:22 PM

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Yes sure

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sir

civic sparrow Mar 13, 2024, 2:22 PM

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for now, whether the sequence begins at 0 or 1 changes what an can be made to mean

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lets say the sequence begins at 1

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then an can be said to mean the "nth term in the sequence"

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because the indices matches up with the way youd naturally count with 1

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the first term is a1
the second term is a2
the third term is a3
etc.
therefore the nth term is an

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now if you want to calculate a series for this,

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you call the first term a1 = 5/10

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you call the ratio r = 1/10

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and n in this case is the sixth term, 5/100000

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from there,

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,,a_1\cdot\frac{1-r^{n+1}}{1-r}\text{ is correct}

brittle lichenBOT Mar 13, 2024, 2:24 PM

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mtt07734

halcyon flume Mar 13, 2024, 2:24 PM

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You mean 5/1.000.000, I guess

civic sparrow Mar 13, 2024, 2:24 PM

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yea

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now take a look at what you calculated instead

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you did a combination of things oddly that you still havent corrected up until now

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first,

halcyon flume Mar 13, 2024, 2:26 PM

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So if i'm not wrong a1 is a0 in my formula because they both represent 5/10(the first number)

civic sparrow Mar 13, 2024, 2:26 PM

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no

halcyon flume Mar 13, 2024, 2:26 PM

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Oof big F

civic sparrow Mar 13, 2024, 2:26 PM

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because if you think thats the only issue, youre in for a nasty surprise later on

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you shouldve pointed out the n

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first

civic sparrow Mar 13, 2024, 2:26 PM

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civic sparrow first,

for now though as a precursor,

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you should be doing r^N instead of 10^N

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that shows your intuition for how this works, and what youre actually doing, arent aligned

halcyon flume Mar 13, 2024, 2:27 PM

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OMG im sorry

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But that thing you took is the one I didn't use anymore

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because see:

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Ill show you

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One second

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pls

halcyon flume Mar 13, 2024, 2:28 PM

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halcyon flume Ill show my calculation 1 sec pls

a

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If you click on "a" then scroll to the original picture from my calculations

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My latest calculation start at 2 lines down from where you got that screenshot from

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I might resend the picture with my latest calculation. I know the -4 was wrong.

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The same picture but cut

civic sparrow Mar 13, 2024, 2:30 PM

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you should just start a new page and have it be the calculations you know should work

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along with what you think would reasonably justify it

halcyon flume Mar 13, 2024, 2:31 PM

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Because that first picture of my calculations have 2 differen calculations the first one is totally etrong

civic sparrow Mar 13, 2024, 2:31 PM

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for example if you think this is correct, you should leave it in the new page

halcyon flume Mar 13, 2024, 2:31 PM

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See right top corner

civic sparrow Mar 13, 2024, 2:31 PM

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I said to make a new page

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beause this still has the exact same issue

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new page please

halcyon flume Mar 13, 2024, 2:32 PM

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Yes I know

civic sparrow Mar 13, 2024, 2:32 PM

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then dont point out a corner that's still just as wrong as the picture I showed

halcyon flume Mar 13, 2024, 2:32 PM

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civic sparrow Mar 13, 2024, 2:32 PM

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this is still wrong

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please create a new page instead of reusing an existing one

halcyon flume Mar 13, 2024, 2:32 PM

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Wait give me 15/20 minutes please, going to eat

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Or like im already eating

halcyon flume Mar 13, 2024, 3:29 PM

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I have a new page

#Calculating row geometric sequence