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culligan water softener service - NBX Soluciones

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 For $ r = 2 $:

📌 rac{32 - 1}{2 - 1} = 31 \quad \Rightarrow \quad 3 \cdot 31 = 93 < 300

📌 For $ r = 3 $:

📌 rac{243 - 1}{3 - 1} = rac{242}{2} = 121 \quad \Rightarrow \quad 3 \cdot 121 = 363 > 300

📌 Thus, $ r = 3 $ satisfies the condition, and since $ r = 2 $ does not, the smallest integer $ r $ is $ oxed{3} $.

📌 Question: A primatologist observes that the number of vocalizations a primate group makes each hour follows the recurrence $ v_n = 2v_{n-1} - 7 $, with $ v_1 = 10 $. What is the value of $ v_5 $?

📌 We compute the terms step-by-step using the recurrence $ v_n = 2v_{n-1} - 7 $, $ v_1 = 10 $:

📌 $ v_2 = 2(10) - 7 = 20 - 7 = 13 $

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