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MDelauney
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Sujet du message: Calculer Uo et la raison r?  Publié: Lun Avr 18, 2011 12:11 am |
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Inscrit le: Ven Mars 25, 2011 4:38 am
Messages: 14
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U5+U6+U7= -27 et U9= -15
Calculer Uo et la raison r.
Jai commencé par faire U9= Uo + 9r = -15
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ifetekil
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Sujet du message: Calculer Uo et la raison r? Publié: Lun Mai 30, 2011 12:13 am |
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Inscrit le: Mer Mars 30, 2011 5:35 am
Messages: 7
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on a u0 + 9r = -15
u0 + 6r = -9
deux equa. deux inconnus :
solution : r = -2 et U0= 3
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wuwifegsah
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Sujet du message: Calculer Uo et la raison r? Publié: Lun Mai 30, 2011 6:09 am |
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Inscrit le: Mar Mars 29, 2011 3:12 pm
Messages: 36
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Suite artihmétique
U5 + U6 + U7 <=> U0 + 5r + U0 + 6r + U0 + 7r = 3U0 + 18r = -27 <=> U0 + 6r = -9
U9= -15 <=> U0 + 9r = -15
Systme déquations deux inconnues :
U0 + 6r = -9
U0 + 9r = -15
A toi de jouer ;)
See ya
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AgobartA
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Sujet du message: Calculer Uo et la raison r? Publié: Lun Mai 30, 2011 11:25 am |
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Inscrit le: Mer Avr 06, 2011 4:29 pm
Messages: 22
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Bonjour,
U(5) + U(6) + U(7) = -27
U(9) = -15
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Si ta suite est arithmétique:
U(n) = U(0) + n.r
U(5) + U(6) + U(7) = -27
U(0) + 5r + U(0) + 6r + U(0) + 7r = 3.U(0) + 18r = -27
U(0) + 6r = -9
U(9) = U(0) + 9r = -15
Do le systme:
U(0) + 6r = -9
U(0) + 9r = -15
3r = -6
r = -2
U(0) = -9 - 6r = -9 + 12 = 3
Do la solution:
U(0) = 3et r = -2
= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
Simplement,
Dragon.Jade :-)
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CRye
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Sujet du message: Calculer Uo et la raison r? Publié: Ven Juin 03, 2011 7:59 pm |
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Inscrit le: Dim Mars 27, 2011 4:17 am
Messages: 16
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Salut!
Données :
------------------------------ U(5) + U(6) + U(7) = -27 ( 1)
------------------------------ U(9) = -15
On sait que :
------------------------------[U(5) +U(7)]/2 = U(6)
ce qui donne
------------------------------- U(5) +U(7) = 2 U(6)
ce qui donne
------------------------------ U(5) +U6)+U(7) = 3U(6) = -27
ce qui donne
------------------------------ U(6) = -27/3
ce qui donne
------------------------------ U(6) = -9
ce qui donne
----------------------------- U(o) + 6r = -9 (2)
On sait que
----------------------------- U(9) = -15
ce qui donne
----------------------------- U(o) + 9r = -15 (3)
Calcul de la raison r
On pose
---------------------------- ( 3 ) - ( 2 )
ce qui donne
------------------------------ U(o) +9r - U(o) - 6r = 3r
ce qui donne
------------------------------ 3r = -15 + 9
ce qui donne
----------------------------- 3r = - 6
ce qui donne
------------------------------- r = -6/3
ce qui donne
------------------------------- r = -2
Calcul de U(o)
On sait :
------------------------------ U(6) = U(o) + 6r
et
------------------------------- U(6) = -9
et
------------------------------- r = -2
ce qui donne
------------------------------- U(o) + 6(-2)= -9
ce qui donne
------------------------------ U(o) -12 = -9
ce qui donne
----------------------------- U(o = -9 +12
ce qui donne
----------------------------- U(o) = 3
Vérification
------------------------------ U(o) = 3
------------------------------ r = -2
---------------------------- U(5) = 3-10
ce qui donne
---------------------------- U(5) = -7
---------------------------- U(6) = -9
---------------------------- U(7) = 3 -14
ce qui donne
----------------------------- U(7) = -11
ce qui donne
---------------------------- U(5) +U(6)+ U(7) = -27
ce qui donne
---------------------------- -7 -9-11 = -27
ce qui donne
---------------------------- -27 = - 27 vrai
---------------------------- U(9) = -15
ce qui donne
----------------------------U(o) -9*2 = -15
ce qui donne
---------------------------- 3 -18 = -15
ce qui donne
---------------------------- -15=-15 vrai
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