2016 AIME II Problem 9

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

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.