House Of Cards

Algebra Level 2

Consecutive towers are built, as shown in the figure above.

The \(1^\text{st}\) tower has one floor made of two cards.
The \(2^\text{nd}\) tower has two floors made of seven cards.
The \(3^\text{rd}\) tower has three floors made of fifteen cards, and so on.

How many cards will the \(1000^\text{th}\) tower have?

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