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Home » Peggie Martin Conquered the Rose: The Spinning Move Every Climber Needs to Master Now! - Midis

Peggie Martin Conquered the Rose: The Spinning Move Every Climber Needs to Master Now! - Midis

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Question:** A zoologist studying animal migration patterns observes that certain species return every few years, forming a sequence similar to an arithmetic progression. How many of the first 50 positive integers are congruent to 3 (mod 7)?

📌 We seek integers \( n \) such that \( n \equiv 3 \pmod{7} \). The sequence of such integers is \( 3, 10, 17, \ldots \).

📌 This is an arithmetic sequence with the first term \( a = 3 \) and common difference \( d = 7 \). The general term is given by:

📌 n_k = 3 + 7(k-1) = 7k - 4

📌 We require \( n_k \leq 50 \):

📌 7k - 4 \leq 50

📌 7k \leq 54

📌 k \leq \frac{54}{7} \approx 7.71

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