# 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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