The sum of the first \( n \) terms of the arithmetic progression is equal to half the sum of the next \( n \) terms of the same progression. Find the ratio of the sum of the first \( 3 n \) terms of the progression to the sum of its first \( n \) terms

Exercice 1 1) Compléter avec l'un des symboles : \( \epsilon ; \notin ; \subset \) ou \( \notin \) \( \{0 ;-7 ; 12\} \ldots \ldots \mathbb{N}^{*} ; \frac{5 \pi-\pi}{2 \pi-\pi} \ldots . \mathbb{Q} ;\left\{-1 ; \frac{18}{6} ; \sqrt{36} ;-7\right\} \ldots . \mathbb{Z} ; \frac{7}{3} \ldots \ldots \) ID 2) donner l'écriture scientifique : \( A=\frac{4 \times 300^{2} \times\left(2 \times 10^{-6}\right)^{-2}}{(0.01)^{-3}} \)

Для матриць A та В знайти матриці: 1. \( \mathrm{A}+\mathrm{B} \); 2. \( 2 \mathrm{~A} ; \) 3. \( \mathrm{A}-\mathrm{B} ; \) 4. A * B \( A=\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right) ; \quad B=\left(\begin{array}{ccc}-1 & 0 & 1 \\ 2 & -3 & 4\end{array}\right) \)

Determine the values of \( x \) and \( y \), in the equation: \( \frac{x-1}{3+i}+\frac{y-1}{3-i}=i \). Solve the following equations: i) \( 2^{2 x+1}=3^{2 x-5} \quad \) ii) \( \log _{2} x-\log _{2} y=2 \) \( \log _{2}(x-2 y)=3 \) In a senior secondary school, 80 students play hockey or football. The number that plays football is 5 more than twice the number that play hockey. If 15 students play both games and every student in the schoo plays at least one game, find the number of students that play football.

In the expansion \( \left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^{n} \) if the ratio between the seventh term from the beginning to the seventh term from the end \( 1: 6 \), then \( n \) equals \( \begin{array}{llll}\text { (a) } 7 & \text { (b) } 8 & \text { (c) } 9 & \text { (d) } 10\end{array} \)

Solve for \( a \) in the proportion. \[ \begin{array}{l}\frac{19}{a}=\frac{9.5}{6} \\ a=\square\end{array} \]