Find The Center

Three numbers are said to be in Arithmetic Progression if the consecutive terms differ by same value(common difference).

Hence, $(4-x)-(x-4)=x-(4-x)$

$\Rightarrow 2(4-x)=x+(x-4)$

$\Rightarrow 8-2x=2x-4$

$\Rightarrow 4x=12$

$\Rightarrow x=\boxed{3}$

The common difference between two consecutive terms of an arithmetic progression is always equal

$\begin{aligned} (x-4)-(4-x) &= (x) - (4 - x) \\ 8 - 2x &= 2x - 4 \\ 4x &= 12 \\ x &= \boxed{3} \end{aligned}$