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\( 50 = \frac12 \times 10 \times \textHeight \). - AdVision eCommerce

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question:** A plant biologist discovers a growth pattern in a drought-resistant crop where the number of new root branches per week follows the sequence: 2, 5, 8, 11, ... What is the sum of the number of root branches produced in the first 30 weeks?

📌 Solution:** The sequence 2, 5, 8, 11, ... is arithmetic with first term \( a = 2 \) and common difference \( d = 3 \).

📌 The sum \( S_n \) of the first \( n \) terms of an arithmetic sequence is:

📌 S_n = \frac{n}{2} (2a + (n - 1)d)

📌 For \( n = 30 \):

📌 S_{30} = \frac{30}{2} \left(2 \cdot 2 + (30 - 1) \cdot 3 \right) = 15 \left(4 + 29 \cdot 3 \right) = 15 (4 + 87) = 15 \cdot 91 = 1365

📌 Thus, the total number of root branches produced in the first 30 weeks is:

📌 \boxed{1365}

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