Question 680379: What is the next 4 numbers in this pattern
1,5,13,26,45,71
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I'm sure you meant to say:
"What are the next 4 numbers in this pattern?" I don't care if this is math; grammar, spelling, and punctuation still count.
Use the method of common differences.
1 5 13 26 45 71
\ / \ / \ / \ / \ /
4 8 13 19 26
\ / \ / \ / \ /
4 5 6 7
\ / \ / \ /
1 1 1
It took 3 iterations of taking the differences to find where the differences are common. Hence, the series is modeled by a 3rd degree polynomial.
\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d)
Since \ =\ 1) :
Since \ =\ 5) :
Likewise
and
Solve the 4X4 system for the ordered quadruple 
Once you have the values of a, b, c, and d, you can write the function that results in the  term by plugging those values into:
From there it is a simple matter of calculating the values of ) , ) , ) , and )
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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