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Home » The sum formula: \( S_n = racn2 (2a + (n-1)d) \) - 500apps

The sum formula: \( S_n = racn2 (2a + (n-1)d) \) - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Find the smallest three-digit number congruent to 4 or 7 modulo 9.

📌 Smallest three-digit number: 100

📌 \( 100 \div 9 = 11 \times 9 = 99 \), remainder 1 → \( 100 \equiv 1 \pmod{9} \) → exclude

📌 \( 101 \equiv 2 \)

📌 \( 102 \equiv 3 \)

📌 \( 103 \equiv 4 \) → valid

📌 So \( D = 103 \)

📌 Check: \( 103 \equiv 4 \pmod{9} \), and \( 4^3 = 64 \equiv 1 \pmod{9} \

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