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#151 2015-09-29 16:14:13
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 60 (three parts (ii) and (iii) are correct! - (i) I made a mistake in the problem)
Exellent, bobbym!
SP # 61. Find the sum of first 15 terms of each of the following sequences having 'n'th term as
.
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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#152 2015-09-29 20:04:37
- 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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#153 2015-09-29 20:25:35
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
SP # 62. In an Arithmetic Progression, the sum of first 'n' terms is
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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#154 2015-09-29 21:14:48
- 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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#155 2015-09-29 21:42:08
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 62 is correct! Flawless!
SP # 63. Let there be an Arithmetic Progression with first term 'a', common difference 'd', If
denotes its 'n'th term and the sum of first n terms, find(i) n and , if a = 5, d = 3, and
(ii) n and a, if , d = 2, and .
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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#156 2015-10-04 22:40:52
- 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.
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#157 2015-10-04 23:34:06
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 63 (all four parts) are correct1 Excellent, bobbym!
SP # 64. (i) How many terms of the Arithmetic Progression 9, 17, 25, ... must be taken so that their sum is 636?
SP # 64. (ii) How many terms of the Arithmetic Progression 63, 60, 57, , ... must be taken so that their sum is 693?
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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#158 2015-10-05 23:18:26
- 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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#159 2015-10-05 23:37:16
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 64 (i) and (ii) [12] and [21,22] respectively are correct! Excellent!
SP # 65. Find the sum of all natural numbers between 1 and 100, which are 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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#160 2015-10-06 13:25:26
- 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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#161 2015-10-06 15:31:08
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 65 is perfect! Immaculate!
SP # 66. Find the sum of all odd integers between
(i) 0 and 50
(ii) 100 and 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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#162 2015-10-06 20:06:22
- 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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#163 2015-10-06 20:14:47
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 66 (both parts) is correct! Good work!
SP # 67. Find the sum of all odd integers between 1 and 1000 which are 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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#164 2015-10-07 12:02:07
- 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.
Offline
#165 2015-10-07 13:49:48
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 67 is perfect! Excellent!
SP # 68. Find the sum of all integers between 100 and 550, which are divisible by 9.
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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#166 2015-10-07 18:13:22
- 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
#167 2015-10-07 18:42:02
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP# 68 is perfect! Good work!
SP # 69. The first term and the last term of an Arithmetic Progression are 17 and 350 respectively. If the common difference is 9, how many terms are there and what is their sum?
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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#168 2015-10-07 20:16:52
- 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
#169 2015-10-07 21:32:40
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 69 (both parts) are correct! Brilliant!
SP # 70. The third term on an Arithmetic Progression is 7 and the seventh term exceeds three times the third term by 2. Find the first term, the common difference, and the sum of first 20 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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#170 2015-10-08 04:42:51
- 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
#171 2015-10-08 07:58:44
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 70 (three parts) are all correct! Excellent!
SP # 71. Find the sum of the first
(i) 11 terms of the Arithmetic Progression 2, 6, 10, 14, ....
(ii) 13 terms of the Arithmetic Progression -6, 0, 6, 12, ...,,
(iii) 51 terms of the Arithmetic Progression whose second term is 2 and fourth term is 8.
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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#172 2015-10-09 03:39:53
- 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
#173 2015-10-10 01:15:59
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 71 (all three parts) is / are correct! Brilliant!
SP # 72. Find the sum first 20 terms of the sequence whose 'n'th term is
.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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#174 2015-10-10 02:59:24
- 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.
Offline
#175 2015-10-10 23:18:23
- Jai Ganesh
- Administrator
- Registered: 2005-06-28
- Posts: 48,384
Re: Series and Progressions
Hi bobbym,
The solution SP # 72 is correct! Splendid!
SP # 73. Find the sum of the first 25 terms of an Arithmetic Progression whose 'n'th term is given by
.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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