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An eco-friendly architectural firm is designing a "stepped" garden for the side of a skyscraper. To ensure every plant gets enough sunlight, they are increasing the variety of solar-powered LED planters on each floor as they go higher.
The variety of planters installed on the first five floors is as follows:
\(2, 5, 10, 17, 26...\)
The Question:
1. Identify the Pattern: Based on the sequence provided, what is the mathematical rule governing the increase in planters?
2. Find the Next Term: How many planters will be required for the 6th floor?
3. The Odd One Out: If the foreman mistakenly ordered \(39\) planters for the \(7\)th floor, is he correct based on the sequence?
4. If not, what should the correct number be?
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