Complex Sequence

Algebra Level 4

Let f ( x ) f(x) be a polynomial of degree 4 such that:

x x f ( x ) f(x)
1 10
2 0
3 0
4 10
5 -10

Find the value of f ( 6 ) − f ( 7 ) f(6)-f(7) .


The answer is 360.

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1 solution

Rishabh Jain
Mar 13, 2016

Using Method of Differences n n f ( n ) D 1 ( n ) D 2 ( n ) D 3 ( n ) D 4 ( n ) 1 10 − 10 10 0 − 40 2 0 0 10 − 40 − 40 3 0 10 − 30 − 80 − 40 3 0 10 − 30 − 80 − 40 4 10 − 20 − 110 − 120 − 40 5 − 10 − 130 − 230 6 − 140 − 360 7 − 500 \begin{array}{c}n n & f(n) & D_{1}(n) & D_{2}(n) & D_{3}(n) & D_{4}(n) \\ 1 ~& 10 & -10 & 10 & 0 & -40 \\ 2 ~& 0 & 0 & 10 & -40 & -40 \\ 3 & 0 & 10 & -30 & -80 & -40 \\ 3 & 0 & 10 & -30 & -80 & -40 \\ 4 & 10 & -20 & -110 & -120 & -40 \\ 5 & -10 & -130 & -230 \\ 6 & -140 & -360 \\ 7 & -500\end{array} ∴ f ( 6 ) − f ( 7 ) = − 140 − ( − 500 ) = 360 \Large \therefore~f(6)-f(7)=-140-(-500)=\boxed{360}

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I did not understand your method

ritik agrawal - 4 years ago

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See the linked wiki at the top of the solution

Rishabh Jain - 4 years ago

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