# What kind of sequence is that?

Algebra Level 4

Let $$a_1,a_2,\ldots$$ be an arithmetic progression and let $$b_1,b_2,\ldots$$ be a non-constant geometric progression.

We define the arithmetic-geometric progression $$c_1,c_2,\ldots$$ such that $$c_k = a_k \cdot b_k.$$

If $$c_1 = 1,$$ $$c_2 = 2,$$ and $$c_3=3,$$ what is the value of $$c_5$$?

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