28P22

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1. Pour tout entier naturel $n$ non nul: \[u_{n+1} = u_n + (-4) = u_n - 4.\]

2. Donc: \[\begin{aligned} u_2 &= u_1 - 4 = 31 - 4 = 27\;;& \\ u_3 &=u_2 - 4 = 27 - 4 = 23\;;& \\ u_4 &= u_3 - 4 = 23 - 4 = 19.& \end{aligned}\]

3. Pour tout entier naturel non nul $n$: \[u_n = u_1 + (n-1)r = 31 -4(n-1).\]

4. Donc : \[\begin{aligned} u_9 &=31 - 4(9-1) = 31 - 4\times 8 = -1\;;& \\ u_{18}&=31 - 4(18-1) = 31 - 4\times 17 = -37\;;& \\ u_{24}&=31 - 4(24 -1) = 31 - 4\times 23 = -61.& \end{aligned}\]

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code : 22