Diketahui suku ke 2 dan sukuke 9 suatu barisan aritmatika adalah 5 dan 19 tentukan suku ke 7 dan jumlah sampai suku ke 20
Barisan Aritmatika
Un = a + (n – 1) b
U2 = a + (2 – 1) b = 5
a + b = 5 …(1)
U9 = a + (9 – 1) b = 19
a + 8b = 19 …(2)
•》 eliminasi pers (1) dan (2)
a + b = 5
a + 8b = 19
________ –
-7b = -14
b = 2
a + b = 5
a + 2= 5
a = 3
▪》 U7 = …?
U7 = a + (7 – 1) b
U7 = 3 + 6 (2)
U7 = 3 + 12 = 15
▪》 S20 = …?
Sn = (n/2) (2a + (n – 1) b)
S20 = (20/2) ( 2(3) + (20 – 1) 2 )
S20 = 10 (6 + 38)
S20 = 10 (44) = 440
Diketahui:
U2 = a + b = 5
U9 = a + 8b = 19
Ditanyakan:
U7 dan S20 = … ?
Penyelesaian:
beda barisan
8b – b = 19 – 5
7b = 14
b = 2
suku pertama
a + 8b = 19
a + 8(2) = 19
a + 16 = 19
a = 3
U7 = a + 6b
U7 = 3 + 6 (2)
U7 = 3 + 12
U7 = 15
Sn = n/2 (2a + (n – 1) b
S20 = 20/2 (2.3 + (20 – 1) 2
S20 = 10 (6 + 38)
S20 = 10 (44)
S20 = 440
Pelajari Lebih Lanjut:
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Detil Jawaban
Kelas: 9
Mapel: Matematika
Bab: Barisan dan Deret Bilangan
Kode: 9.2.2
Kata Kunci: Barisan, Deret, aritmatika