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#26 2006-03-07 21:21:01

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Excellent, krassi_holmz!

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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#27 2006-03-11 03:46:02

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

SP # 7

k is the Arithmetic Mean of two quantities x and y. p and q are two Geometric Means between x and y. Prove that

p³ + q³ = 2kxy.

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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#28 2015-09-05 00:47:39

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,419
Website

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#29 2015-09-05 09:14:04

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi zetafunc,

The solution is correct! Good work!

SP #8. Find the common difference and write the next three terms of the Arithmetic Progression 3, -2, -7, -12...

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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#30 2015-09-05 10:26:07

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,419
Website

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#31 2015-09-05 11:01:24

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi zetafunc,

The solutiom SP # 8 is correct! Neat work!

SP # 9. Find the sum of first 30 terms of an Arithmetic Progression whose second term is 2 and seventh term is 22.

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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#32 2015-09-05 21:40:07

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#33 2015-09-06 02:12:20

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi bobbym,

The solution SP # 9 is correct! Well done!

SP # 10. Find the sum of 20 terms of the Arithmetic Progression 1, 4, 7, 10, ...

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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#34 2015-09-06 03:31:27

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: Series and Progressions

Only a friend tells you your face is dirty.

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#35 2015-09-06 05:20:10

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#36 2015-09-06 11:25:01

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi math9maniac and bobbym,

The solution SP # 10 is correct! Keep it up!

SP # 11. Find the sum of all three digit natural numbers, which are divisible by 7.

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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#37 2015-09-06 16:45:41

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#38 2015-09-06 17:56:19

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi bobbym,

The solution SP # 11 is correct! Excellent!

SP # 12. Find the sum of all odd integers between
2 and 100 divisible by 3.

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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#39 2015-09-07 00:34:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#40 2015-09-07 03:23:41

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: Series and Progressions

Only a friend tells you your face is dirty.

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#41 2015-09-07 09:13:05

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi bobbym and math9maniac,

SP # 13. How many terms of the series 54, 51, 48, ...be taken so that their sum is 513!

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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#42 2015-09-07 19:48:02

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: Series and Progressions

Only a friend tells you your face is dirty.

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#43 2015-09-07 19:55:16

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#44 2015-09-08 18:08:50

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi math9maniac and bobbym,

The solution SP # 13 is correct! Excellent, math9maniac and bobbym!

SP # 14. The sum of the third and seventh terms of an Arithnetic Progression is 6 and their products is 8. Find the sum of first sixteen terms of the Arithmetic Progression. (Give both solutions).

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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#45 2015-09-08 20:58:28

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: Series and Progressions

Only a friend tells you your face is dirty.

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#46 2015-09-09 00:06:14

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi math9maniac,

Regarding SP # 14, I shall wait for the solution(s) of bobbym and zetafunc. Please wait for some time.

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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#47 2015-09-09 00:15:26

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 443

Re: Series and Progressions

Hi ganesh,

I'm ok with your decision. Thanks.

Only a friend tells you your face is dirty.

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#48 2015-09-09 16:48:52

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

#49 2015-09-10 15:47:20

Jai Ganesh
Registered: 2005-06-28
Posts: 43,591

Re: Series and Progressions

Hi math9maniac and bobbym,

The solution #SP # 14 is correct, bobbym! Brilliant!

SP # 15. How many terms are there in the sequence 3, 6, 9, 12, ..., 111?

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.

Offline

#50 2015-09-10 20:22:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Series and Progressions

Hi;

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline