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April 29, 2024, 05:57:29 pm
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Author Topic: Questions  (Read 10094 times)  Share 

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droodles

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Re: Questions
« Reply #15 on: May 11, 2008, 03:04:37 pm »
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LOL...
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Ahmad

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Re: Questions
« Reply #16 on: May 11, 2008, 10:09:52 pm »
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Since dcc stole my favourite method - I propose an elementary one.



Multiply both sides by



Rearranging, then decreasing n,







...



Summing up LHS, and RHS respectively, noting that most of the terms on the LHS cancel, and subbing in t_1, while summing the geometric series on the right,



Changing n+1 to n, while cleaning up,


« Last Edit: May 11, 2008, 10:16:10 pm by Ahmad »
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Glockmeister

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Re: Questions
« Reply #17 on: May 11, 2008, 10:11:43 pm »
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except I can't read latex.
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Ahmad

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Re: Questions
« Reply #18 on: May 11, 2008, 10:17:28 pm »
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You don't need to, anymore. on the forum broke for a short while, but it's fine now.
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Mandark: Please, oh please, set me up on a date with that golden-haired angel who graces our undeserving school with her infinite beauty!

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Mao

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Re: Questions
« Reply #19 on: May 11, 2008, 10:21:55 pm »
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sorry dcc, but i like Ahmad's method more than yours :P

i only got lost once :P (as opposed to 20000000 times)
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dcc

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Re: Questions
« Reply #20 on: May 11, 2008, 10:28:39 pm »
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Quote from: Mao on May 11, 2008, 10:21:55 pm
sorry dcc, but i like Ahmad's method more than yours :P

i only got lost once :P (as opposed to 20000000 times)

It's actually Ahmad's method, but i stole it :P
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Ahmad

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Re: Questions
« Reply #21 on: May 11, 2008, 10:32:12 pm »
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Generating function are cool though Mao, google generatingfunctionology if you're any interested.

For simple recurrences it's kind of like using integration instead of the 1/2bh formula to find the area of a triangle, but then it's much more general, just like integration is.
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Rosie

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Re: Questions
« Reply #22 on: May 16, 2008, 11:55:26 am »
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Is anyone familiar with the Fibonacci sequence. I have a question.

In the fibonacci sequence, t7=13, t9=34 and t10=55
Name the terms represented by:
t11+2t12+t13

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Mao

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Re: Questions
« Reply #23 on: May 16, 2008, 06:04:22 pm »
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plato

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Re: Questions
« Reply #24 on: May 19, 2008, 11:45:45 pm »
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Quote from: Rosie on May 16, 2008, 11:55:26 am
Is anyone familiar with the Fibonacci sequence. I have a question.

In the fibonacci sequence, t7=13, t9=34 and t10=55
Name the terms represented by:
t11+2t12+t13


While Mao has simplified your expression to the term as you had requested, you may then want this value of . Use your stated values of and (you could ignore the value of !)

If the sequence is related to a Fibonnaci sequence, then each term is the sum of the TWO terms before it. Therefore,




and so
« Last Edit: May 20, 2008, 12:14:04 am by plato »
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Rosie

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Re: Questions
« Reply #25 on: May 20, 2008, 06:43:03 pm »
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Number Patterns
Q1. A gardener moves a load of sand by emptying barrow loads of sand at points along a straight line. The first drop-off point is 20 metres from where the sand was originally dumped. The remaining loads of sand are then dropped off at five-metre intervals along the line.

After 15 barrow loads, all the sand has been moved. How far in total would the gardener have to walk to move all the sand and then return to the point where the sand was originally dumped?


Q2. A car purchased on 1 June 2005 loses value at a depreciation rate of 20% per year. The original purchase price was $25 000. The value of the car in dollars on 1 June 2010 will be:


   
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Odette

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Re: Questions
« Reply #26 on: May 20, 2008, 07:56:56 pm »
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Q1.
t1= 20
d= 5
n= 16
Using the formula tn= a + (n-1)d
                        t16= 20 + (15 x 5)
                            = 20 + 75
                            = 95
*I'm not 100% sure have done these in a while lol... may have interpreted the question wrong.

Q2.
P= 25000
R= 0.8
n= 5

Using depreciation formula- A= PR^n
                                     A= 25000 x 0.8 ^5
                                     A= $ 8192
Hope that helps ^_^
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/0

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Re: Questions
« Reply #27 on: May 20, 2008, 11:22:21 pm »
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Quote from: Odette on May 20, 2008, 07:56:56 pm
Q1.
t1= 20
d= 5
n= 16
Using the formula tn= a + (n-1)d
                        t16= 20 + (15 x 5)
                            = 20 + 75
                            = 95
*I'm not 100% sure have done these in a while lol... may have interpreted the question wrong.

I think it's a sum formula instead of a nth term formula, because it asks u to find the total distance travelled, i.e the total length of

---->
<----
------>
<------
--------->
<---------

etc... 15 times back n forth

So to find the total disatnce in one direction then a = 20, d = 5, n = 15



But since we have only counted the total distance he walks one way, we need to multiply be 2 because he has to return to pick up more sand => total distance is 1650m
I think that's right...
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Odette

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Re: Questions
« Reply #28 on: May 21, 2008, 08:12:34 am »
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Quote from: DivideBy0 on May 20, 2008, 11:22:21 pm
Quote from: Odette on May 20, 2008, 07:56:56 pm
Q1.
t1= 20
d= 5
n= 16
Using the formula tn= a + (n-1)d
                        t16= 20 + (15 x 5)
                            = 20 + 75
                            = 95
*I'm not 100% sure have done these in a while lol... may have interpreted the question wrong.

I think it's a sum formula instead of a nth term formula, because it asks u to find the total distance travelled, i.e the total length of

---->
<----
------>
<------
--------->
<---------

etc... 15 times back n forth

So to find the total disatnce in one direction then a = 20, d = 5, n = 15



But since we have only counted the total distance he walks one way, we need to multiply be 2 because he has to return to pick up more sand => total distance is 1650m
I think that's right...
Yep yep, sorry missed that part of the question lolz... you're right ^_^
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Rosie

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Re: Questions
« Reply #29 on: May 22, 2008, 06:08:19 pm »
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Q. In an arithmetic sequence, a=250 and d=26. The first term in this sequence to exceed 500 is:
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