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Found problems: 1

2016 AIME Problems, 9
Tags: AIME , AIME II , 2016 AIME II , 2016 AIME II Problem 9 , Sequences
The sequences of positive integers $1,a_2,a_3,\ldots$ and $1,b_2,b_3,\ldots$ 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 $c_k$.