Show that `|x+1x+2x+a x+2x+3x+b x+3x+4x+c|=0` where `a ,\ b ,\ c` are in A.P.

Explanation

To show that the determinant

\[
D = \begin{vmatrix}
x + 1 & x + 2 & x + a \\
x + 2 & x + 3 & x + b \\
x + 3 & x + 4 & x + c
\end{vmatrix}
...