Question 516344: Use the Method of Finite Differences to find a function for the following sequences. Explain your process.
a. 9, 5, -5, -21, . . .
b. 2.5, 6, 13.5, 25, . . .
Ok...This is what I have done.
For "a" there is a second common difference of -6, and for "b" there is a second common difference of 4. Now I have forgotten how to use the method of finite differences. I remember learning something about generating the sequence by using:
a_n+1 = a_n + (the second common difference)n + something?
But I’m not sure this is what I need to use…I’m sure if I could just see “a” done I can do “b”. Thanks in advance for the help!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website!
Use the Method of Finite Differences to find a function for the following sequences. Explain your process.
a. 9, 5, -5, -21, . . .
b. 2.5, 6, 13.5, 25, . . .
Ok...This is what I have done.
For "a" there is a second common difference of -6, and for "b" there is a second common difference of 4. Now I have forgotten how to use the method of finite differences. I remember learning something about generating the sequence by using:
a_n+1 = a_n + (the second common difference)n + something?
But I’m not sure this is what I need to use…I’m sure if I could just see “a” done I can do “b”. Thanks in advance for the help!
----------------
a. 9, 5, -5, -21, .
;;;;;-4;;-10;-16
;;;;;;;-6;;;-6
----
Form f(x) = ax^2+bx+c
(1) = a + b + c = 9
f(2) = 4a +2b + c = 5
f(3) = 9a+3b + c = -5
---------------------------
Solve for a,b,c,d
I solved the system using a Matrix Method to get:
a = -3; b = 5; c = 7
==================================
Equation f(x) = -3x^2 + 5x + 7
f(1) = 9
f(2) = 5
f(3) = -5
==================
Cheers,
Stan H.
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The site below illustrates the method of Finite Differences
http://mathforum.org/library/drmath/view/53223.html
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