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Question Number 30355 by mondodotto@gmail.com last updated on 21/Feb/18

	Answered by $@ty@m last updated on 21/Feb/18

	$120$
	Commented by mondodotto@gmail.com last updated on 21/Feb/18

	$solution please$
	Commented by MJS last updated on 21/Feb/18

	$a_{n} = {(- 1)}^{n} \times (n - 1)!$
	Answered by MJS last updated on 21/Feb/18

	$or - 206$ $if a_{n} = - \frac{65}{24} n^{4} + \frac{119}{4} n^{3} - \frac{2719}{24} n^{2} + \frac{697}{4} n - 89$
	Commented by mondodotto@gmail.com last updated on 21/Feb/18

	$more explaination please$
	Commented by MJS last updated on 21/Feb/18
	$5 given points determine a polynome function P_1 = [(1),((−1)) ] P_2 = [(2),(1) ] P_3 = [(3),((−2)) ] P_4 = [(4),(6) ] P_5 = [(5),((−24)) ] P_n = [(x_n ),(y_n ) ] with y_n =ax_n ^4 +bx_n ^3 +cx_n ^2 +dx_n +e lead to a linear system which can be solved for {a, b, c, d, e}$
	$5 given points determine a$ $polynome function$ $P_{1} = [\begin{matrix} 1 \\ - 1 \end{matrix}] P_{2} = [\begin{matrix} 2 \\ 1 \end{matrix}] P_{3} = [\begin{matrix} 3 \\ - 2 \end{matrix}]$ $P_{4} = [\begin{matrix} 4 \\ 6 \end{matrix}] P_{5} = [\begin{matrix} 5 \\ - 24 \end{matrix}]$ $P_{n} = [\begin{matrix} x_{n} \\ y_{n} \end{matrix}] with y_{n} = {a x}_{n}^{4} + {b x}_{n}^{3} + {c x}_{n}^{2} + {d x}_{n} + e$ $lead to a linear system which can$ $be solved for {a, b, c, d, e}$
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