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**ganesh****Moderator**- Registered: 2005-06-28
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SP # 1

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

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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**ganesh****Moderator**- Registered: 2005-06-28
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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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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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**ganesh****Moderator**- Registered: 2005-06-28
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Character is who you are when no one is looking.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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That's better.

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**ganesh****Moderator**- Registered: 2005-06-28
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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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**krassi_holmz****Real Member**- Registered: 2005-12-02
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642?

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**ganesh****Moderator**- Registered: 2005-06-28
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**krassi_holmz****Real Member**- Registered: 2005-12-02
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I want MORE!!!

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**ganesh****Moderator**- Registered: 2005-06-28
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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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**ganesh****Moderator**- Registered: 2005-06-28
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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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**Ricky****Moderator**- Registered: 2005-12-04
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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?

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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If we count this we get the sum :

I may be wrong.

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**ganesh****Moderator**- Registered: 2005-06-28
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Character is who you are when no one is looking.

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**ganesh****Moderator**- Registered: 2005-06-28
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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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**mathsyperson****Moderator**- Registered: 2005-06-22
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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.

Why did the vector cross the road?

It wanted to be normal.

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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Einstein would say:

It depends on it's speed.

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**ganesh****Moderator**- Registered: 2005-06-28
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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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**Ricky****Moderator**- Registered: 2005-12-04
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*Last edited by Ricky (2006-03-05 17:06:02)*

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**ganesh****Moderator**- Registered: 2005-06-28
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**Well done. Ricky!**

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**ganesh****Moderator**- Registered: 2005-06-28
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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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**mathsyperson****Moderator**- Registered: 2005-06-22
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Why did the vector cross the road?

It wanted to be normal.

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**ganesh****Moderator**- Registered: 2005-06-28
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**You are correct, mathsyperson! Well done! **

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**krassi_holmz****Real Member**- Registered: 2005-12-02
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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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