# To the cinema

Jane at 8 am got message that all 1093 school pupils will 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 all the children in school know that they will go to the cinema?

Result

x = 10:20 h

#### Solution:

$a_1 = 1 \ \\ q = 3 \ \\ S_n = 1093 \ \\ \ \\ 1093 = \dfrac{1 -3^n}{1-3} \ \\ 1-3^n = -2186 \ \\ 3^n = 2187 \ \\ n \log 3 = \log 2187 \ \\ n = 7 \ \\ \ \\ x = 8+20/60\cdot 7 = 10:20 \ \text{h}$

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