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
