Kamis, 01 Januari 2015

Barisan dan Deret



Barisan adalah daftar urutan bilangan dari kiri ke kanan yang mempunyai karakteristik atau pola tertentu. Setiap bilangan dalam barisan merupakan suku dalam barisan. 
Deret adalah Penjumlahan suku-suku dari suatu barisan disebut deret. Jika U1,U2,U3,…..Un maka U1 + U2 + U+… +Un.
Definisi baris aritmatika :
Jika beda antara suatu suku apa saja dalam suatu barisan dengan suku sebelumnya adalah suatu bilangan tetap b maka barisan ini adalah barisan aritmatika. Bilangan tetap b itu dinamakan beda dari barisan.
Polanya : a, a+b, a+2b, a+3b,…..,a+(n-1)b
Dengan
o   a = U1= Suku pertama       
o   b = beda
o   n = banyaknya suku
o   U= Suku ke-n
      Definisi barisan geometri :
Jika rasio antara suku apa saja dalam suatu barisan dengan suku sebelumnya merupakan suatu bilangan tetap maka barisan tersebut adalah barisan geometri.bilangan tetap r disebut rasio dari barisan.

Rumus jumlah n suku pertama dari deret geometri adalah :
            Sn = a( 1- r) / 1 – r , jika r < 1 dan
                        Sn = a( rn - 1) / r – 1 , jika r > 1

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