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The next two terms in this series are -124xy, -412xy.

Here’s my reason.

Let f(x)=ax³+bx²+cx+d be the function that defines each term where 0≤x≤3 and:

f(0)=-2, f(1)=-12, f(2)=9, f(3)=-6.


f(1)=a+b+c+d=-12, so a+b+c=-10;





f(3)-3f(1)-3[f(2)-2f(1)]=6a=26-93=-67, a=-67/6. 2b=31-6a=31+67=98, b=49.



f(4)=-124, f(5)=-412.

Now insert xy to create the next two terms.


by Top Rated User (721k points)

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