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#376 2015-12-24 03:41:55
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
I gave up on this one, but your formula checks out! How did you solve this?
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#377 2015-12-24 03:58:36
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Series and Progressions
The summation calculus is one way.
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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#378 2015-12-24 14:21:43
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi Relentless and bobbym,
Excellent, bobbym!
SP #173. Find three consecutive terms of an Arithmetic Progression whose sum is 18 and the sum of their squares is 140.
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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#379 2015-12-24 14:32:06
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hello!
The formulas are equivalent for SP #172
Last edited by Relentless (2015-12-24 14:32:29)
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#380 2015-12-24 14:48:24
- 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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#381 2015-12-24 15:03:37
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi Relentless and bobbym,
The solution SP#173 is correct! Good work!
SP#174. Find the common difference of the Arithmetic Progression:
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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#382 2015-12-24 15:39:39
- 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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#383 2015-12-24 16:47:08
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi bobbym,
The solution SP#174 is correct! Neat work!
SP#175. The sum of the first 'n' terms of an Arithmetic Progression is
. Find the 'n'th term of this Arithmetic Progression.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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#384 2015-12-24 17:48:44
- 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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#385 2015-12-25 17:58:55
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi bobbym,
The solution SP#175 is correct! Excellent!
SP#176. The sum of the first seven terms of an Arithmetic Progression is 63 and the sum of the next seven terms is 161. Find the 28th term of this Arithmetic Progression.
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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#386 2015-12-25 20:11:00
- 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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#387 2015-12-25 22:02:34
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hi! I liked this one. Despite its simplicity, it requires abstraction
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#388 2015-12-25 22:42:39
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi bobbym and Relentless,
The solution SP#176 is correct! Excellent!
SP#177. The sum of first 'n' terms of an Arithmetic Progression is
. Find the 'n'th term of this Arithmetic Progression.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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#389 2015-12-25 22:59:19
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hey!
Took me way too long to confirm, but here it is
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#390 2015-12-26 03:58:47
- 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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#391 2015-12-26 13:09:40
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi Relentless and bobbym,
The solution SP#177 is correct! Brilliant!
SP#178. If the 10th term of an Arithmetic Progression is 21 and the sum of its first ten terms is 120, find its 'n'th term.
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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#392 2015-12-26 15:49:55
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hey!
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#393 2015-12-26 16:34:57
- 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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#394 2015-12-27 16:47:24
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi Relentless and bobbym,
The solution SP#178 is correct! Excellent!
SP#179. Sum of the first 14 terms of an Arithmetic Progression is 1505 and its first term is 10. Find its 25th term.
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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#395 2015-12-27 18:17:04
- 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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#396 2015-12-27 18:33:01
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hi;
It's a bit of a giveaway when you are given the first term 
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#397 2015-12-28 17:18:32
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi bobbym and Relentless,
The solution SP#179 is correct! Wonderful!
SP#180. A man saved $32 during the first year, $36 is the second year and in this way, he increases his savings by $4 every year. Find in what time his savings will be $200.
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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#398 2015-12-28 18:10:45
- 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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#399 2015-12-28 18:58:45
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hello!
I'm sure the answer varies depending on leap year cycles, but I think even I am not pedantic enough to work that out right now.
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#400 2015-12-29 16:42:30
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 46,294
Re: Series and Progressions
Hi bobbym and Relentless,
The solution SP#180 is correct! Good work!
SP#181. Find the number of terms of the Arithmetic Progression -12, -9, -6, ..., 21. If 1 is added to each term of this Arithmetic Progression, then find the sum of all terms of the Arithmetic Progression thus obtained.
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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