Is it bad math style to use one letter for indexing two objects?

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Is $$\sum_{i\in I_1} a_i + \sum_{i \in I_2} b_i$$ or $$\prod_{i\in I_1} a_i \cdot \prod_{i \in I_2} b_i$$ confusing or bad math? Should I rather use $j$ for indexing the $b$'s?