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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(0)=d=-2.

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

f(2)=8a+4b+2c=11;

f(3)=27a+9b+3c=-4.

f(2)-2f(1)=6a+2b=31;

f(3)-3f(1)=24a+6b=26.

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

c=-10-(a+b)=-10-(-67/6+49)=-287/6.

f(x)=-67x³/6+49x²-287x/6-2.

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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