Thursday, May 30, 2013

Deret Geometri


Sn = a(rn-1)/r-1 , jika r>1
     = a(1-rn)/1-r , jika r<1
S = a/(1-r)
Ket:
a = suku awal
r = rasio
n = banyak suku
contoh:
1.      Diketahui barisan geometri dengan U3 = 27 dan U5 = 243. Berapakah 6 suku pertama deret tersebut?

Solusi :
1.      U3 = a .  r3-1   = a . r2 = 27                      27 = U1 . (3)3-1
U5 = a .  r5-1   = a . r4 = 243                    27 = U1 . 32
27 = U1 . 9
U5/U3 = a . r4 / a . r2 = 243/27                 U1 = 27 : 9 = 3
r2 = 9                                                         U1 = 27 : 9 = 3
 r = 3
 S15 = 3 ( 36 - 1) / 3-1 = 3 (729-1) / 2 = 3 (728) /2 = 1092

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