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#351 2015-12-21 00:13:47
- Relentless
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- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hi ganesh, the series you have written for #162 is 4n + 7, so only term 1 is the same.
The 20 terms are actually 11, 7, 3, -1, -5, -9 ... -57, -61, -65. Their sum is -540. I don't know how the answers diverged so widely, but I am absolutely sure of this one.
Regarding the formula, all you have to do is change d to -4 instead of +4.
Last edited by Relentless (2015-12-21 00:23:07)
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#352 2015-12-21 02:46:23
- Jai Ganesh
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- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi.
Excellent, Relentless!
SP #164. The sum of the seven terms of an Arithmetic Progression is 182. If its fourth and seventeenth terms are in the ratio 1:5, find the first four terms 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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#353 2015-12-21 03:15:06
- Relentless
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- Registered: 2015-12-15
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Re: Series and Progressions
Just a start:
20d + 5x = 17d + x
x = -3d/4
Where x is the 0th term (a = x + d = d/4).
Sum of first seven terms: 91d/4
Oh that's a bit more than a start haha 
Fun fact: The 17th and 82nd terms are also in the ratio 1:5. And the difference 82 - 17 is 5 times the difference between 17 - 4. Perhaps a new question is to show the next 3 predicted instances of this apparent pattern to try to confirm it! 
Last edited by Relentless (2015-12-21 03:42:29)
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#354 2015-12-21 04:53:18
- 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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#355 2015-12-21 15:03:53
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Relentless and bobbym,
The solution SP #164 is correct! Neat work!
SP #165. If the 'n'th term of the Arithmetic Progression 9,7,5,... is the same as the 'n'th term of the Arithmetic Progression 15,12,9,.., find 'n'.
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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#356 2015-12-21 15:25:16
- Relentless
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- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
-2n + 11 = -3n + 18
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#357 2015-12-21 16:34:32
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Relentless,
The solution SP #165 is correct! Well done!
SP #166. Find the sum of the first 2n terms of the following series:
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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#358 2015-12-21 18:00:21
- Relentless
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- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
I only just wrote the sums and stared at them, but I think:
Last edited by Relentless (2015-12-21 18:26:44)
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#359 2015-12-21 18:26:19
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Relentless,
The solution SP #166 is correct! Brilliant!
SP #167. Find the common ratio and the general term of the sequence
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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#360 2015-12-21 18:35:27
- Relentless
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- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hi!
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#361 2015-12-21 20:32:37
- 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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#362 2015-12-21 23:35:20
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Relentless and bobbym,
The solution
The solution is partially correct, Relentless! Good work!
The solution is perfect, bobbym! Excellent!
SP #168. The sum of the first three terms of a Geometric Progression is 13 and sum of their squares is 91. Find the three terms.
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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#363 2015-12-22 00:33:07
- 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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#364 2015-12-22 00:47:38
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
This was a fun problem (constructing and solving simultaneous equations for a and r)
Last edited by Relentless (2015-12-22 01:00:52)
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#365 2015-12-22 14:53:57
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi bobbym and Relentless,
The solution SP #168 is correct! Good work!
SP #169. Which term of the following Arithmetic Sequence is 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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#366 2015-12-22 14:57:50
- Relentless
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- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
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#367 2015-12-22 15:41:29
- 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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#368 2015-12-23 00:44:53
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Relentless and bobbym,
The solution #169 is perfect! Excellent, Relentless and bobbym!
SP #170. How many terms are there in the following Arithmetic Progressions?
.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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#369 2015-12-23 01:30:30
- Monox D. I-Fly
- Member
- From: Indonesia
- Registered: 2015-12-02
- Posts: 2,000
Re: Series and Progressions
Actually I never watch Star Wars and not interested in it anyway, but I choose a Yoda card as my avatar in honor of our great friend bobbym who has passed away.
May his adventurous soul rest in peace at heaven.
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#370 2015-12-23 03:02:44
- Relentless
- Member
- Registered: 2015-12-15
- Posts: 631
Re: Series and Progressions
Hello!
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#371 2015-12-23 12:48:29
- 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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#372 2015-12-23 16:33:59
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi Monox D. I-Fly, Relentless, and bobbym,
The solution (two parts) is SP#170 are correct! Excellent, Monox D. I-Fly, Relentless, and bobbym!
SP #171. Find the sum of the series:
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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#373 2015-12-23 17:25:20
- 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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#374 2015-12-23 21:06:34
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,423
Re: Series and Progressions
Hi bobbym,
The solution SP#171 is correct! Brilliant!
SP#172. Find the sum of 'n' terms of the series 7 + 77 + 777 + ...
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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#375 2015-12-24 03:34:19
- 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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