Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#1 2014-03-08 21:22:36
What am I doing wrong? #Arithmetic_Progressions
The ratio of the sum of n terms of two APs is (3n +4):(2n + 7). Find the ratio of their m[sup]th[/sup] terms.
Let the sum of n terms of the two APs be (3n +4)x and(2n + 7)x for some proportionality constant x.
mth term of the first AP = Sum of m terms - Sum of (m-1) terms = (3m + 4) x - (3(m-1) + 4)x = 3x
mth term of the second AP = Sum of m terms - Sum of (m-1) terms = (2m + 7) x - (2(m-1) + 7) x = 2x
Ratio of the mth terms of the APs = 3:2
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#2 2014-03-08 22:33:03
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
With numbers substituted, the ratio is not constant but a function of m. I'm still trying to work out what function. Watch this space. 
Later edit: arrhh, the light dawns. Your x is not a constant but also is a function of n. Tricky. 
Bob
Last edited by Bob (2014-03-08 22:35:23)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#3 2014-03-08 23:14:05
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
By trial and improvement I have found a pair of sequences with the ratio property. With AP1 the first term is 1 and the common difference 4/9 and for AP2 the first term is 7/9 and the common difference is 2/3
The terms ratio is not constant.
Bob
Last edited by Bob (2014-03-08 23:16:33)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#4 2014-03-08 23:26:37
Re: What am I doing wrong? #Arithmetic_Progressions
What am I doing wrong? 
I think the uestion itself is wrong. The ratio of the sums should have contained a second power of m. Ain't it??
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#5 2014-03-08 23:33:02
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
Just trying an idea. ........................
didn't work but I got close by T and I.
this is my near answer:
ratio = (7m+6.5)/(10m+0.5)
Got to cut the grass now. Maybe my brain will keep working during this break.
Bob
Last edited by Bob (2014-03-08 23:45:13)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#6 2014-03-09 01:29:37
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: What am I doing wrong? #Arithmetic_Progressions
Hello Agnishom;
Bobbym showed me how to do these a long time ago. 
Hope that is right.
Last edited by ElainaVW (2014-03-09 01:30:32)
Offline
#7 2014-03-09 01:31:39
Re: What am I doing wrong? #Arithmetic_Progressions
Hello Agnishom;
Bobbym showed me how to do these a long time ago.
Hope that is right.
I am getting that if I do it that way, but why isn't this one working?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#8 2014-03-09 01:38:07
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: What am I doing wrong? #Arithmetic_Progressions
Hello;
I'm using an algorithmic method that he showed me. I don't know what is wrong with your method. M says, use methods that work.
Last edited by ElainaVW (2014-03-09 01:41:07)
Offline
#9 2014-03-09 01:39:11
Re: What am I doing wrong? #Arithmetic_Progressions
I do not think that anyone can show me an AP that follows this conditions.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#10 2014-03-09 01:42:07
- ElainaVW
- Member
- Registered: 2013-04-29
- Posts: 580
Re: What am I doing wrong? #Arithmetic_Progressions
You mean two AP's.
Last edited by ElainaVW (2014-03-09 01:42:21)
Offline
#11 2014-03-09 01:46:05
Re: What am I doing wrong? #Arithmetic_Progressions
yeah. you can show them?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#12 2014-03-09 01:58:34
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
Hi;
How about these two, but there are an infinite number of them.
Hi Elaina;
Wunderbar! You learn well grasshopper. I had to look it up deep in the ole notes. Also, over here I am bobbym not Bobbym.
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
#13 2014-03-09 02:22:11
Re: What am I doing wrong? #Arithmetic_Progressions
What about my method?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#14 2014-03-09 02:33:49
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
Hi;
You are treating the numerator and the denominator as the arithmetic sum of each. There could have been more terms in both and got cancelled.
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
#15 2014-03-09 02:35:03
Re: What am I doing wrong? #Arithmetic_Progressions
I do not understand.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#16 2014-03-09 02:39:18
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
(3n +4):(2n + 7)
Maybe, 3n+4 is not the sum of the first AP nor is 2n+7. They could have been 5(3n+4) and 5(2n+7) now the 5's get cancelled. The ratio stays the same but not the individual sum. Could have been anything on the top and bottom.
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
#17 2014-03-09 02:46:44
Re: What am I doing wrong? #Arithmetic_Progressions
That is why I multiplied them with x in the first post.
Let the sum of n terms of the two APs be (3n +4)x and(2n + 7)x for some proportionality constant x.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#18 2014-03-09 02:53:06
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
But x is probably a function of m not a constant, because there could have been (m+1) on the top and bottom.
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
#19 2014-03-09 04:45:18
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
hi,
That's it exactly as I said way back. The ratio varies with n, so there is not a constant x.
I've just got back from a walk and wrote out my mental thoughts. bobbym's two sequences are the same as mine. By varying the first term (ie change the 1 to 'a') you will generate another pair. The common difference has to be 4a/9 for that sequence (it took a page of algebraic fractions to prove that !!!) and the common difference for the second is then 2a/3.
I have my own expression for the required ratio, but it fills 4 lines of my paper at the moment as I haven't yet simplified it.
Bob
Last edited by Bob (2014-03-09 04:48:07)
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#20 2014-03-09 04:46:32
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
Hi Bob;
See post #6.
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
#21 2014-03-09 04:49:43
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
hi bobbym,
Yes, I saw that. My expression may reduce to that after some fairly major simplifying. Or I may just accept that answer.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#22 2014-03-09 04:50:17
Re: What am I doing wrong? #Arithmetic_Progressions
Thank you, I already know how to do that solution
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#23 2014-03-09 04:53:34
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,643
Re: What am I doing wrong? #Arithmetic_Progressions
OK. I'll save paper and have a break.
Bob
Children are not defined by school ...........The Fonz
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob
Offline
#24 2014-03-09 04:53:37
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: What am I doing wrong? #Arithmetic_Progressions
If need be I will post the entire method that she used.
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
#25 2014-03-09 04:56:29
Re: What am I doing wrong? #Arithmetic_Progressions
OK. I'll save paper and have a break.
Bob
Hi;
Why do you cut grass?
@bobbym, okay. but I'll see you tomorrow
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline