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Home » Farm Clipart You’ll Want to Save & Share—Free Download Inside! - Treasure Valley Movers

Farm Clipart You’ll Want to Save & Share—Free Download Inside! - Treasure Valley Movers

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 2Question: What is the remainder when the sum of the first 100 even numbers is divided by 7?

📌 Solution: The first 100 even numbers form an arithmetic sequence: $2 + 4 + 6 + \dots + 200$. The sum is $S = \frac{100}{2} \times (2 + 200) = 50 \times 202 = 10100$. To find $10100 \mod 7$, divide 10100 by 7: $7 \times 1442 = 10094$, so the remainder is $10100 - 10094 = 6$. $\boxed{6}$

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