Need help please
Okay
need the degree and equation: 
 n   1  2  3  4  5
f(n)11 21 35 53 75 
i think the degree is 4 and it is linear
but that is as far as I can get
Help Please 
Thanks
llo


n     1    2     3     4     5  
f(n) 11   21    35    53    75

To find the degree:
Make a difference table, by finding the
difference of each adjacent pair, writing
the differences until you find a line of
differences that are all the same.

n     1     2      3     4     5  
f(n) 11    21     35    53    75
1       10     14    18    22
2           4      4     4 

                 
It took 2 lines of differences to find
a line on which all the numbers are the 
same, so we know to assume a polynomial 
of degree 2 (a quadratic):

f(n) = An² + Bn + C 

Since f(1) = 11,

f(1) = A(1)² + B(1) + C = 11
f(1) = A + B + C = 11

Since f(2) = 21

f(2) = A(2)² + B(2) + C = 21
f(2) = A(4) + B(2) + C = 21
f(2) = 4A + 2B + C = 21

Since f(3) = 35

f(3) = A(3)² + B(3) + C = 35
f(3) = A(9) + B(3) + C = 35
f(3) = 9A + 3B + C = 35

So we have the system of equations:

 A +  B + C = 11
4A + 2B + C = 21
9A + 3B + C = 35

Do you know how to solve that system of
equations with matrices?  If not post
again asking how.  The solution is

A=2, B=4, C=5

So

f(n) = An² + Bn + C so

f(n) = 2n² + 4n + 5

Edwin


 

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