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Home » So \( k \equiv 18 \pmod35 \) - Londonproperty

So \( k \equiv 18 \pmod35 \) - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Somme = \(\frac{33}{2} \times (3 + 99) = \frac{33 \times 102}{2} = 1683\).

📌 Somme des multiples de 5 : \(5 + 10 + \ldots + 95\).

📌 Le premier terme est 5, le dernier \(95\), la raison 5. Résolvez \(5 + (n-1) \times 5 = 95 \Rightarrow n = 19\).

📌 Somme = \(\frac{19}{2} \times (5 + 95) = \frac{19 \times 100}{2} = 950\).

📌 Somme des multiples de 15 (pour éviter le double comptage) : \(15 + 30 + \ldots + 90\).

📌 Premier terme 15, dernier 90, raison 15. Résolvez \(15 + (n-1) \times 15 = 90 \Rightarrow n = 6\).

📌 Somme = \(\frac{6}{2} \times (15 + 90) = 3 \times 105 = 315\).

📌 Somme totale = \(1683 + 950 - 315 = 2318\).

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Substitute into the first equation: \(2x + 3(4x - 5) = 6\).
Simplify: \(2x + 12x - 15 = 6\), so \(14x = 21\).
Solve: \(x = 1.5\).
Substitute back to find \(y\): \(y = 4(1.5) - 5 = 1\).
#### \(x = 1.5\), \(y = 1\)
If the sum of the first \(n\) natural numbers is given by \(\frac{n(n+...
Set up the equation: \(\frac{n(n+1)}{2} = 210\).
Multiply by 2: \(n(n+1) = 420\).
Solve \(n^2 + n - 420 = 0\) using the quadratic formula:
\(n = \frac{-1 \pm \sqrt{1 + 1680}}{2} = \frac{-1 \pm 41}{2}\).

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