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#1 2006-02-27 02:20:06
- Jai Ganesh
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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
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#2 2006-02-27 03:00:43
- krassi_holmz
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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)
IPBLE: Increasing Performance By Lowering Expectations.
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#3 2006-02-27 16:41:27
- Jai 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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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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)
IPBLE: Increasing Performance By Lowering Expectations.
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#5 2006-02-27 18:05:48
- Jai Ganesh
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Re: Series and Progressions
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#6 2006-02-27 18:16:13
- krassi_holmz
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Re: Series and Progressions
That's better.
IPBLE: Increasing Performance By Lowering Expectations.
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#7 2006-02-28 16:14:27
- Jai 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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#8 2006-02-28 17:56:26
- krassi_holmz
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Re: Series and Progressions
642?
IPBLE: Increasing Performance By Lowering Expectations.
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#9 2006-02-28 19:43:27
- Jai Ganesh
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Re: Series and Progressions
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#10 2006-02-28 19:45:45
- krassi_holmz
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Re: Series and Progressions
I want MORE!!!
IPBLE: Increasing Performance By Lowering Expectations.
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#11 2006-03-01 18:02:41
- Jai 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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#12 2006-03-02 17:43:42
- Jai 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?
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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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.
IPBLE: Increasing Performance By Lowering Expectations.
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#15 2006-03-03 02:27:52
- Jai Ganesh
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Re: Series and Progressions
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#16 2006-03-03 02:36:28
- Jai 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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#17 2006-03-03 23:33:10
- mathsyperson
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Re: Series and Progressions
SP #4: the ball is dropped, so it doesn't travel anywhere.
If you're being picky like that, then technically it travels 6m. 
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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Re: Series and Progressions
Einstein would say:
It depends on it's speed.
IPBLE: Increasing Performance By Lowering Expectations.
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#19 2006-03-05 16:49:00
- Jai 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'.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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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
- Jai Ganesh
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Re: Series and Progressions
Well done. Ricky! 
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#22 2006-03-06 18:29:26
- Jai Ganesh
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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.
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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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
- Jai Ganesh
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Re: Series and Progressions
You are correct, mathsyperson! Well done!
It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.
Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.
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#25 2006-03-07 19:38:54
- krassi_holmz
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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
IPBLE: Increasing Performance By Lowering Expectations.
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