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\[ = 3n^2 - n - 2 \] - iBuildNew

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 \]Question: A primatologist observes that the number of vocalizations made by a troop of chimpanzees follows an arithmetic sequence over five consecutive days. If the total number of vocalizations over the five days is 120, and the difference between the number of vocalizations on the last day and the first day is 16, what is the number of vocalizations on the third day?

📌 Solution: Let the five terms of the arithmetic sequence be $ a - 2d, a - d, a, a + d, a + 2d $, where $ a $ is the middle (third) term and $ d $ is the common difference.

📌 The sum of the five terms is:

📌 The difference between the last and first term is:

📌 Since the third term is $ a $, the number of vocalizations on the third day is:

📌 \boxed{24}

📌 Question: An anthropologist studying trade records from an ancient civilization finds that the price of five identical obsidian tools and three carved stone beads equals 43 gold coins, while the price of two tools and five beads equals 31 gold coins. How many gold coins does one bead cost?

📌 Solution: Let $ t $ be the price of one tool and $ b $ be the price of one bead.

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