If a, b and are such that $$ak^2 + bk + c \neq 0$$ for some k and if the determinant of the matrix $$\begin{bmatrix}a & b & ak+b \\b & c & bk + c\\ak+b & bk+c & 0 \end{bmatrix}$$ is zero then a, b, c are in

A

an arithmetic progression

B

a harmonic progression

C

an arithmetic — geometric series

D

a geometric progression