1.
Let the numbers 22, bb, cc be in an A.P. and
A=[1112bc4b2c2]A=\begin{bmatrix} 1 & 1 & 1 \\ 2 & b & c \\ 4 & b^{2} & c^{2} \end{bmatrix}

If det(A)[2,16]\det(A)\in[2,16], then cc lies in the interval: