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#1 2016-09-01 02:14:20

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Progression Into Mathematics, #1

1. The sum of the first 2 terms of an geometric series is 7. The sum of the first 6, however, is 91. What is the sum of the first 4 terms?

2. Find the sum of gif.latex?%5Cfrac%7B1%7D%7B11%7D+%5Cfrac%7B2%7D%7B11%5E%7B2%7D%7D+%5Cfrac%7B1%7D%7B11%5E%7B3%7D%7D+%5Cfrac%7B2%7D%7B11%5E%7B4%7D%7D.....%3Dx..(Please put your solution in fractional forme.)

3. By adding the same constant A to 20, 50 and 100, a geometric progression results. Find the common ratio and the constant A.

4. The first three numbers of a set A form a arithmetic progression. The last three form a geometric progression. The sum of the first and last elements of A is 16. The sum of the middle two numbers is 12.Find these 4 elements, but be warned that there is more than one solution. BONUS to anyone who finds both of them.
All elements of A are integers.

5. The sum of the first 2011 terms of a GEOMETRIC PROGRESSION is 200. The sum of the first 4022, however, is 380, Find the sum of the first 6033 terms.

6. Find the coefficient of the term that contains x^4 in the expansion of gif.latex?%28x%20-%20%5Cfrac%7B1%7D%7B2x%7D%29%5E%7B10%7D

7. Find the least positive integer whose digits add to a multiple of 27 yet the number itself is not a multiple
of 27. For example, 87999921 is one such number.

8.How many non-congruent isosceles triangles (including equilateral triangles) have positive integer side
lengths and perimeter less than 20?

9. The Bobbym Lizard Garden Store sells grass seed in ten-pound bags and fifteen-pound bags. Yesterday half
of the grass seed they had was in ten-pound bags. This morning the store received a shipment of 27 more
ten-pound bags, and now they have twice as many ten-pound bags as fifteen-pound bags. Find the total
weight in pounds of grass seed the store now has.
10. The zeros of the function f(x) = x^2-ax+3a are integers. What is the sum of the possible values of a. If there are NONE, respond with NONE.


The integral of hope is reality.

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#2 2016-09-01 02:20:52

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

Re: Progression Into Mathematics, #1

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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#3 2016-09-01 04:06:21

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

bobbym wrote:

Hi;

Hello, I vastly disagree with you on 1, I could not get a negative solution.
Well done, and a is indeed an integer.


The integral of hope is reality.

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#4 2016-09-01 04:54:27

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1



Last edited by thickhead (2016-09-01 05:36:58)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#5 2016-09-01 05:04:47

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

Re: Progression Into Mathematics, #1

Hello, I vastly disagree with you on 1,

People who disagree with me are eaten by gators, which seems fair.

I am sticking with the answer for one. There is also another answer for one which I did not put down.


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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#6 2016-09-01 06:28:15

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

thickhead wrote:



Well done, thickhead, but I am getting a similar but different answer. Let me verify mine again..


The integral of hope is reality.

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#7 2016-09-01 06:30:44

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

bobbym wrote:

Hello, I vastly disagree with you on 1,

People who disagree with me are eaten by gators, which seems fair.

I am sticking with the answer for one. There is also another answer for one which I did not put down.

Bobbym, I know you fear your nefarious lizard neighbors so I will infest your house with lizards. tongue


The integral of hope is reality.

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#8 2016-09-01 06:54:52

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

Re: Progression Into Mathematics, #1

I have a little lizard running around there right now. It is about three inches long and very fast. It came in when I opened the door about a month ago. I thought he found his way out but he is still in here.

28 is the other answer but the -21, that was the hard one.

Filled in a few more, check post #2.


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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#9 2016-09-01 14:37:24

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#10 2016-09-01 16:33:44

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

I chose common ratio r=sqrt(3) since I thought it would suit the irrational personality of Mathegocart.
But bobbym thought otherwise and chose r=2*sqrt(-1) as he thought there is nothing real but only imaginary value present in Mathegocart.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#11 2016-09-01 17:56:46

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#12 2016-09-01 18:11:41

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

Re: Progression Into Mathematics, #1

There are actually 6 values for a:

{-4, -4, 0, 12, 16, 16}

each one corresponding to a different x. I decided to use the double -4 and 16 in the sum. That is where I got 36. I could not deduce from the question whether doubles were to be considered or not because no where in the question does it say distinct a's. Now, looking at the question and having to guess what Mathegocart wants I would go with 24 too.


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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#13 2016-09-01 18:18:00

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

I missed nothing in the total but curiously I missed a=0!


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#14 2016-09-02 04:14:39

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

thickhead wrote:

I chose common ratio r=sqrt(3) since I thought it would suit the irrational personality of Mathegocart.
But bobbym thought otherwise and chose r=2*sqrt(-1) as he thought there is nothing real but only imaginary value present in Mathegocart.

Irrational? My profound eccentricity is only relative to yours!
I am not real nor imaginary, I am truly complex.
Also I see you have adapted my signature into a more adept one. Too bad there is no LaTeX implementation in the sigs, for it would make for quite a grandeur look!

Last edited by Mathegocart (2016-09-02 04:19:08)


The integral of hope is reality.

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#15 2016-09-02 04:15:49

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

bobbym wrote:

There are actually 6 values for a:

{-4, -4, 0, 12, 16, 16}

each one corresponding to a different x. I decided to use the double -4 and 16 in the sum. That is where I got 36. I could not deduce from the question whether doubles were to be considered or not because no where in the question does it say distinct a's. Now, looking at the question and having to guess what Mathegocart wants I would go with 24 too.

That was the intended solution(24.)


The integral of hope is reality.

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#16 2016-09-02 04:54:42

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

Mathegocart wrote:

Well done, thickhead, but I am getting a similar but different answer. Let me verify mine again..

Where do we differ?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#17 2016-09-02 04:57:57

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

Re: Progression Into Mathematics, #1

All done then?


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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#18 2016-09-02 12:35:27

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

thickhead wrote:
Mathegocart wrote:

Well done, thickhead, but I am getting a similar but different answer. Let me verify mine again..

Where do we differ?

(5)


The integral of hope is reality.

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#19 2016-09-02 12:41:44

Mathegocart
Member
Registered: 2012-04-29
Posts: 1,884

Re: Progression Into Mathematics, #1

Note: I am planning to develop a formidable armada of physics questions.


The integral of hope is reality.

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#20 2016-09-02 12:45:13

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

Re: Progression Into Mathematics, #1

A formidable armada? You have a very good vocabulary.


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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#21 2016-09-02 16:39:48

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

Last edited by thickhead (2016-09-02 16:42:11)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#22 2016-09-02 18:18:27

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

Hi Mathegocart,
I have to admit I am a nut.  My method was too long.In A.P. Groups of terms of same size are also in A.P.
(5)sum of 1st 2011 terms=200
sum of next 2011 terms=380-200=180   D=180 -200 =-20
sum of next 2011 terms=180 -20=160
Sum of first 6033 terms=200 +180+160=540

Last edited by thickhead (2016-09-02 18:19:12)


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#23 2016-09-02 18:54:38

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

Re: Progression Into Mathematics, #1

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

#24 2016-09-02 19:03:09

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Progression Into Mathematics, #1

hi bobbym,
Does Mathegocart agree with you? I have to fight in 2 fronts even if he does not agree with you and not with me also.
Cn=an you find  holes in the 2 methods I have described?


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#25 2016-09-02 19:07:06

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

Re: Progression Into Mathematics, #1

I do not know what Mr. Mathegocart has for an answer yet.

Are you solving for geometric progressions?


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

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