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#1 2006-02-27 02:20:06

ganesh
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Registered: 2005-06-28
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Series and Progressions

SP # 1

If p, q, r are in Arithmetic Progression and x, y, z are in Geometric Progression, show that


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#2 2006-02-27 03:00:43

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Series and Progressions

Let:
p=p
q=p+a
r=p+2a
x=x
y=bx
z=b^2x
Then:

Last edited by krassi_holmz (2006-02-27 03:05:26)


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#3 2006-02-27 16:41:27

ganesh
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Re: Series and Progressions

krassi_holmz, although I don't see any serious mistake in the way you started, I am not fully convinced with the proof. I shall wait for a few more days before posing the solution.


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#4 2006-02-27 17:38:34

krassi_holmz
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Re: Series and Progressions

p,q and r are in Arithmetic prgression, so
q=p+a
r=p+2a, because of the arithmetic progression propeties.
Same for the x,y,z:
y=bx
z=b^2x

Next is just simple arithmetic reduction:



Where's my mistake?

Last edited by krassi_holmz (2006-02-27 17:46:07)


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#5 2006-02-27 18:05:48

ganesh
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Re: Series and Progressions

correct_answer.gif


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#6 2006-02-27 18:16:13

krassi_holmz
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Re: Series and Progressions

That's better.
smile


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#7 2006-02-28 16:14:27

ganesh
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Re: Series and Progressions

SP # 2

The sum of the digits of a three digit number is 12. The digits are in Arithmetic Progression. If the digits are reversed, then the number is diminished by 396. Find the number.


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#8 2006-02-28 17:56:26

krassi_holmz
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Re: Series and Progressions

642?


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#9 2006-02-28 19:43:27

ganesh
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Re: Series and Progressions

correct.gif


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#10 2006-02-28 19:45:45

krassi_holmz
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Re: Series and Progressions

I want MORE!!!


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#11 2006-03-01 18:02:41

ganesh
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Re: Series and Progressions

Here you get!

SP# 3

The sum of an infinite series in Geometric Progression is 57 and sum of their cubes is 9747. Find the series.


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#12 2006-03-02 17:43:42

ganesh
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Re: Series and Progressions

SP # 4

A ball is dropped from a height of 6m and on each bounce it rebounces to 2/3 of its previous height. How far does the ball travel till it stops bouncing?


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#13 2006-03-02 17:52:01

Ricky
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Re: Series and Progressions

SP #4: the ball is dropped, so it doesn't travel anywhere.

But seriously, by traveled, do you mean both positive and negative changes in height?  In other words, do we count the ball going up and down?


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#14 2006-03-03 00:11:41

krassi_holmz
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Re: Series and Progressions

If we count this we get the sum :


I may be wrong.


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#15 2006-03-03 02:27:52

ganesh
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Re: Series and Progressions

excellent.gif


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#16 2006-03-03 02:36:28

ganesh
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Re: Series and Progressions

This is how the problem is solved in a different way.

1. The distance covered in the downward path is an infinite Geometric series with a=6m, r=2/3.
Therefore, S[sub]n=[6/(1-2/3)]=6/(1/3)=18m
2. The distance covered in the upward path is an infinte Geometric series with a=4m, r=2/3.
S[sub]n=[4/(1-2/3)]=4/(1/3)=12m

Total distance = 18m + 12m = 30m.


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#17 2006-03-03 23:33:10

mathsyperson
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Registered: 2005-06-22
Posts: 4,900

Re: Series and Progressions

Ricky wrote:

SP #4: the ball is dropped, so it doesn't travel anywhere.

If you're being picky like that, then technically it travels 6m. tongue


Why did the vector cross the road?
It wanted to be normal.

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#18 2006-03-04 00:47:40

krassi_holmz
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Registered: 2005-12-02
Posts: 1,908

Re: Series and Progressions

Einstein would say:
It depends on it's speed.
tongue tongue


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#19 2006-03-05 16:49:00

ganesh
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Re: Series and Progressions

SP # 5

The first term of a Geometric Progression is 64 and the average of the first and the fourth terms is 140. Find the common ratio 'r'.


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#20 2006-03-05 17:05:52

Ricky
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Re: Series and Progressions

Last edited by Ricky (2006-03-05 17:06:02)


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#21 2006-03-05 17:20:13

ganesh
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Registered: 2005-06-28
Posts: 13,189

Re: Series and Progressions

Well done. Ricky! cool


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#22 2006-03-06 18:29:26

ganesh
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Registered: 2005-06-28
Posts: 13,189

Re: Series and Progressions

SP # 6

A man borrows $5,115 to be repaid in 10 monthly instalments. If each instalment is double the value of the last, find the value of the first and the last instalment.


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#23 2006-03-07 04:19:08

mathsyperson
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Re: Series and Progressions


Why did the vector cross the road?
It wanted to be normal.

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#24 2006-03-07 04:22:56

ganesh
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Posts: 13,189

Re: Series and Progressions

You are correct, mathsyperson! Well done! cool


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#25 2006-03-07 19:38:54

krassi_holmz
Real Member
Registered: 2005-12-02
Posts: 1,908

Re: Series and Progressions

SP#3:



q=57(1-a)
Solving

a=2/3 or a=3/2;
Then q=19 or q=-57/2
But when q=-57/2 the sum is negative, so:
So the answer is:
a=2/3;q=19


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