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Home » \[ (2a + b) - (a + b) = 6 - 5 \] - go-checkin.com

\[ (2a + b) - (a + b) = 6 - 5 \] - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Let the growth rates on the three consecutive days be \(x\), \(x+1\), and \(x+2\). The sum of these rates is:

📌 x + (x+1) + (x+2) = 3x + 3 = 33

📌 Solving for \(x\), we have:

📌 3x + 3 = 33 \implies 3x = 30 \implies x = 10

📌 Thus, the growth rates are \(10\), \(11\), and \(12\) grams per day. The growth rate on the third day is:

📌 \]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:

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