Math
posted by Abigail on .
Help, I can't find the pattern rule for this sequence(eg. 6,3,2,9,18 and the pattern rule is n squared7)
The pattern: 6,28,64,114,178.
What's the pattern rule?
The pattern: 96,84,64,36.
What's the pattern rule?
The pattern: 0,24,216,960.
What's the pattern rule?

These appear to be susceptible to solution using Newton's Divided Difference method.
For the first one,
n: 1 2 3 4 5
f(n): 6 28 64 114 178
d1(n)=f(n+1)f(n): 22 36 50 64
d2(n)=[d1(n+1)d1(n)]/2: 7 7 7 7
The second differences are constant. So, the final function has coefficients from the first entry in each row:
f(n) = 6 + 22(n1) + 7(n1)(n2)
f(n) = 7x^2 + x  2
This is the polynomial of lowest degree which fits all the given data points.
Read up on the method, and you can do the others easily. A web search on "divided difference interpolation formula" reveals lots of articles, and even a calculator at the ucla site. 
pattern rule for
2,3, ___, 7, 11, 13, 17, ___ 
8,9,11,14 , , ,

15,10,5 I need A. B. C. I need the number pattern