Find the missing entry in the following table. | $x$ | $0$ | $1$ | $2$ | $3$ | $4$ | | --- | --- | --- | --- | --- | --- | | $y_x$ | $1$ | $3$ | $9$ | $-$ | $81$ |

Find the missing entry in the following table. | x – Class 12 Business Mathematics Statistics

Question 18 of 37

Find the missing entry in the following table.

$x$	$0$	$1$	$2$	$3$	$4$
$y_x$	$1$	$3$	$9$	$-$	$81$

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Set $\Delta^4 y_0=0$ (four known values $\Rightarrow$ cubic), i.e. $y_4-4y_3+6y_2-4y_1+y_0=0$ , and solve for $y_3=31$ .

Five points are given with one value missing, so we treat the data as a polynomial of degree $3$ ; then the fourth forward difference is zero:

$\Delta^4 y_0=y_4-4y_3+6y_2-4y_1+y_0=0.$ …