# A.P + GP $$\neq$$ A.G.P

Algebra Level 4

Let $$A=\{a_1, a_2, \ldots, a_n\}$$ be a set of the first $$n$$ terms of an arithmetic progression. Similarly, let $$B=\{b_1, b_2, \ldots, b_n\}$$ be a set of the first $$n$$ terms of a geometric progression.

If a new set $$C=A+B=\{a_1+b_1, a_2+b_2, \ldots, a_n+b_n\}$$ and the first four terms of $$C$$ are $$\{0, 0, 1, 0\},$$ what is the $$11^\text{th}$$ term of $$C?$$

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