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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

**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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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.

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

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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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, ...

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

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

Only a friend tells you your face is dirty.

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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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.

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

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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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.

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

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

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

Only a friend tells you your face is dirty.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

Hi bobbym and math9maniac,

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

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

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

Only a friend tells you your face is dirty.

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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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).

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

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

Only a friend tells you your face is dirty.

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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

Hi math9maniac,

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

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

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

Hi ganesh,

I'm ok with your decision. Thanks.

Only a friend tells you your face is dirty.

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

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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**Jai Ganesh****Administrator**- Registered: 2005-06-28
- Posts: 47,828

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?

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

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

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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