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April 17, 2014

April 17, 2014

Posted by **Abigail** on Wednesday, November 2, 2011 at 6:32pm.

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?

- Math -
**Steve**, Thursday, November 3, 2011 at 3:28pmThese 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(n-1) + 7(n-1)(n-2)

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.

- Math -
**Jen**, Friday, May 4, 2012 at 12:30pmpattern rule for

2,3, ___, 7, 11, 13, 17, ___

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