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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

Re: Series and Progressions

Excellent, krassi_holmz! up


It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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
Member
Registered: 2014-05-21
Posts: 1,219
Website

Re: Series and Progressions

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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
Member
Registered: 2014-05-21
Posts: 1,219
Website

Re: Series and Progressions

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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: 372

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline

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

math9maniac
Member
From: Tema
Registered: 2015-03-30
Posts: 372

Re: Series and Progressions


Only a friend tells you your face is dirty.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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: 372

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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: 372

Re: Series and Progressions


Only a friend tells you your face is dirty.

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

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: 372

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
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline

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

ganesh
Moderator
Registered: 2005-06-28
Posts: 20,909

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 is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi. 

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Offline

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

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 104,231

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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.

Offline

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