Define the following terms using difference tables (i). Forward differences (ii). Backward differences (iii). Central differences

Since there are 5 data points, we assume that the fourth-order forward difference is zero, i.e., $\Delta^4 f(x_0) = 0$.

The formula for $\Delta^4 f(x_0)$ is given by:

Let $f(x_0)=4$, $f(x_1)=3$, $f(x_2)=4$, $f(x_3)=y_3$, and $f(x_4)=12$.
Setting $\Delta^4 f(x_0) = 0$:

The missing term in the table is $\text{7}$.