Di-Sequences (Part 2)

Algebra Level pending

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 \(c_k\).

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