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## #1 2013-10-16 09:35:54

ninjaman
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### arithmetic series

hello
I have to answer a question using arithmetic series and im confused about the rearranging of forumlas. I haven't done a lot of this and would really appreciate the help!!!

the question is,
a body falling freely falls 5m in the first second of its motion, 15m in the second, and 25m during the third.

how long will it take to fall 3000m

I have the formula here, Sn = n/2 (2a+(n-1)d),

so with the values that I have, a being 5, d being 10 and Sn being 3000

I did this,  3000*2 = n(10+(n-1)10)

then         6000     = n(100+(n-1))
then                     100-1+n =99+n
so,            6000    = n 99+n
= n^2 +99-99
6000-99 = n^2
5901     = n^2
(sqrt)5901   = (sqrt)n^2

to get,       n = 76.8179 seconds

again im not sure if this is correct so any help would be really appreciated!!!

thanks
all the best
simon:D

## #2 2013-10-16 12:50:47

bobbym

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### Re: arithmetic series

Hi;

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2013-10-16 18:01:41

bob bundy
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### Re: arithmetic series

hi ninjaman

Welcome to the forum.

Your substitution into the formula was OK, but then you made a small slip with the algebra:

I did this,  3000*2 = n(10+(n-1)10)

You should have multiplied the (n-1)10 first like this:

3000*2 = n(10+10n - 10)

Then the bracket simplifies:

3000*2 = n(10n)

Then you have the equation that bobbym has already shown you.

6000 = 10n^2

600 = n^2

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #4 2013-10-16 21:21:02

ninjaman
Member

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### Re: arithmetic series

so expanding the brackets first

I haven't done a lot of math for a while and im getting thrown into the deep end, some of it is cooking my brain!!!
thank you for all your help

can you suggest a good site that shows how to rearrange formula and expand out the brackets. after putting the formula into the search engine, only advanced math sites come up.

all the best simon

## #5 2013-10-16 21:32:56

bob bundy
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### Re: arithmetic series

hi Simon

Lots of people discover this forum without realising there is another site constructed by the same guy called MathsIsFun.

That site is full of really excellent teaching pages covering lots of areas of maths.  The pages are cross-linked so once you've found a page of interest you can quickly go to other related pages or you can use the search.  Here's a couple to get you started:

http://www.mathsisfun.com/algebra/equation-formula.html

http://www.mathsisfun.com/algebra/expanding.html

And you are welcome to come back to the forum if you still want more help.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #6 2013-10-16 21:40:43

bobbym

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### Re: arithmetic series

im getting thrown into the deep end, some of it is cooking my brain!!!

Only zombies like raw brain.Cooked brain, preferably  well done with some lemon or garlic sauce smeared on it is my cup of tea.

If cooked brain is not to your liking then here is what I do. Carefully remove your brain and put it somewhere cool and dry right before doing any math. Works for me.

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.