|
|
| Page 1 of 1 |
|
|
 Posted: Wed, 4th Mar 2015 19:10 Post subject: Quadratic reduction |
|
 |
My college mate gave me the answer to this quadratic reduction equation; now, instead of just using his answer and submitting it, I was to understand how he got the the answer; I've applied his answer and it works, I just don't know how he got to that answer (mine is different).
Find the nth term of the arithmetic sequence 3, 8, 13……
Use the quadratic equation an2 + bn + c = term
n is the term value of the sequence i.e. 1, 2, 3
1. n= 1 gives us:- a + b + c = 3
2. n= 2 gives us:- 4a + 2b + c = 8
3. n= 3 gives us:- 9a + 3b + c = 13
4. Subtract equation 1 from equation 2- gives 3a + b = 5
5. Subtract equation 2 from equation 3- gives 5a + b = 5
6. Subtract equation 4 from equation 5- gives 2a = 0, a = 0
7. Substitute a = 0 into equation 4, gives b = 5
8. Substitute a = 0 and b = 5 into 4 equation 1- gives c = -2
9. Nth term equation from equation 1 and the values for a, b, c- gives us
0 n2 + 5n + (-2) = term gives in terms of n, nth term is 5n – 2
This is what our tutor gave us, I understand it for the most part (this is an example).
We had to apply this to 4, 8, 16 (32, 64, 128).
Now, using the above, I came the answer of 0n² + 4n + 0 = 4n²
My friend came to the answer of 2n² - 2n + 4
His answer is right and mine is wrong; I've read countless formulae on google but, maybe someone here can guide me on how he reached this conclusion.
I'm not asking for hand-outs, I'm asking for help so I can understand how he came to that so I can apply it in future.
|
|
| Back to top |
|
|
|
|
| Posted: Wed, 4th Mar 2015 21:14 Post subject: |
|
|
Once you plug in your new values you have 3 equations with 3 unknowns:
a + b + c = 4
4a + 2b + c = 8
9a + 3b + c = 16
You then do Gauss-Jordan elimination, it's pretty simple and you can google how to do that. You can use the following calculator. It prints out all the steps, just plugin in the numbers above: http://matrix.reshish.com/gauss-jordanElimination.php
You then plugin the values you get from that in any of the above equations and you get the equation for your arithmetic sequence.
|
|
| Back to top |
|
|
|
|
| Posted: Wed, 4th Mar 2015 23:44 Post subject: |
|
|
First of all, thank you for your reply.
Just to clear a few things; I believe this is Geometric as it's a multiple of its former series number.
I have all the calculations done except one little thing that doesn't seem to fit after looking at photo I took of my maths tutor doing it.
He's my final calculations:
2 - 2 + c = 4
This means that my mate bang on; as the above becomes 2n² - 2n + 4
What I noticed in my tutors screen shot, in the example he gave, he did (numbers were different in his example):
6 - 12 + C = 3 + 6
C = 9
From what I gather, he has changed the side of the 6 and added it to the c + 3 to make 9.
However, if you apply this to my sequence of:
2 - 2 + C = 4 - 2 = 2
C = 2
Which is wrong; if I don't do the - 2, if stays as four which is right; my question is, is it necessary to change the side in my equation like he did in the example?
Even without that addition calculation it's looks mathematically sound because 2 - 2 + C = 4 means that C must equate to four.
|
|
| Back to top |
|
|
| Page 1 of 1 |
All times are GMT + 1 Hour |
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
Powered by phpBB 2.0.8 © 2001, 2002 phpBB Group
|
|
 |
|
