Materi : Barisan dan Geometri
Soal Nomor 9
U3 = 6
U5 = 10
[ x = 3 , Ux = 6 ]
[ y = 5 , Uy = 10 ]
Cari Beda
( y - x )b = Uy - Ux
( 5 - 3 )b = 10 - 6
2b = 4
b = 2
Cari Suku Pertama
a = Ux - b( x - 1 )
a = 6 - 2( 3 - 1 )
a = 6 - 2(2)
a = 6 - 4
a = 2
Hasil / Result :
Pola barisan aritmatika
2, 4, 6, 8, 10, ...
Suku Pertama = 2 , Beda = 2
Maka rumus pola : Un = 2n
Maka U8 = 2(8) = 16 { b. }
Soal Nomor 10
[ x = 8 , Ux = 31 ]
[ y = 14 , Uy = 55 ]
Cari Beda
( y - x )b = Uy - Ux
( 14 - 8 )b = 55 - 31
6b = 24
b = 4
Cari Suku Pertama
a = Ux - b( x - 1 )
a = 31 - 4( 8 - 1 )
a = 31 - 4(7)
a = 31 - 28
a = 3
Hasil / Result :
Pola barisan aritmatika
3, 7, 11, 15, 19, ...
Suku Pertama = 3 , Beda = 4
Maka rumus pola : Un = 4n - 1
Maka U22 = 4(22) - 1 = 87 { d. }
Soal Nomor 11
U2 = 5 ⇒ a + b = 5
U4 + U6 = 28 ⇒2a + 8b = 28
Metode Eliminasi
2a + 2b = 10
2a + 8b = 28
__________-
- 6b = -18
[ b = 3 ]
\_____/
a = 5 - b
a = 5 - 3
[ a = 2 ]
Hasil / Result :
Pola barisan aritmatika
2, 5, 8, 11, 14, ...
Suku Pertama = 2 , Beda = 3
Maka rumus pola : Un = 3n - 1
Maka U9 = 3(9) - 1 = 26 { d. }
Soal Nomor 12
U5 + U9 = 44
( a + 4b ) + ( a + 8b ) = 44
2a + 12b = 44
a + 6b = 22 [ U7 ] { c. }
Semoga bisa membantu
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