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Home » Use the Pythagorean theorem: a² + b² = c². - ToelettAPP

Use the Pythagorean theorem: a² + b² = c². - ToelettAPP

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 La séquence est géométrique avec le premier terme \(a = 2\) et la raison \(r = 3\).

📌 Le \(n\)-ème terme est donné par \(a_n = ar^{n-1}\).

📌 Pour le 6ème terme : \(a_6 = 2 \times 3^{5} = 2 \times 243 = 486\).

📌 Trouvez la somme de tous les entiers positifs inférieurs à 100 qui sont divisibles par 3 ou 5.

📌 Utilisez le principe d’inclusion-exclusion :

📌 Somme des multiples de 3 : \(3 + 6 + \ldots + 99\).

📌 Il s’agit d’une série arithmétique avec le premier terme 3, le dernier terme 99, et la raison 3. Le nombre de termes \(n\) est donné en résolvant \(3 + (n-1) \times 3 = 99 \Rightarrow n = 33\).

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

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