Di-Sequences (Part 2)

The sequences of positive integers $1,a_2,a_3,...$ and $1,b_2,b_3,...$ are increasing arithmetic and geometric sequences respectively. Let $c_n=a_n+b_n$ . There is an integer $k$ such that $c_{k-1}=100$ and $c_{k+1}=1000$ . Compute $c_k$ .