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Home » - \frac32(1) = -\frac12. - DNSFLEX

- \frac32(1) = -\frac12. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Now, add these results:

📌 + 5 + 1 + 3 = 12

📌 Next, find the remainder of 12 when divided by 6:

📌 \equiv 0 \pmod{6}

📌 Thus, the remainder is \(\boxed{0}\).

📌 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:

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