To the cinema

Jane at 8 AM got a message that all 1093 school pupils would go to the cinema. Within 20 min she said it to the three friends. Each of them again for 20 minutes said to the other three. In this way, the message spread further. At what time do all the schoolchildren know they will go to the cinema?

Result

x = 10:20 h

Step-by-step explanation:

$$\begin{gathered} a_1=1 \\ q=3 \\ {S}_n=1093 \\ {t}_0=20\text{min}\to \text{h}=20:60\text{h}=0.33333\text{h} \\ {S}_n=\frac{1-3^n}{1-3}=1093 \\ 1-3^n=-2186 \\ {3}^n=2187 \\ n\log 3=\log 2187 \\ n=\log 2187/\log 3=7 \\ x=8+n\cdot t_0=8+7\cdot 0.3333=10.33333=10:20\text{h} \end{gathered}$$

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