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- 1. http://www.free-powerpoint-templates-design.com Barisan dan Deret Kelas X Tahun 2024/2025 SMA Negeri 8 Surakarta
- 2. Agenda Style Barisan dan Deret Aritmatika 1 3 Pola Bilangan 4 Deret Tak Hingga Barisan dan Deret Geometri 2
- 3. 1. Pola Bilangan Perhatikan susunan dan jumlah noktah berikut. 1 12 4 22 9 32 16 42 25 52 ? ?2 Pola Bilangan Persegi ? Un = n2
- 4. Perhatikan susunan dan jumlah noktah berikut. 1 3 6 10 15 ?
- 5. Jika kita perhatikan, susunan-susunan bilangan tersebut mempunyai pola dan aturan tertentu. Susunan yang demikian dinamakan Barisan Bilangan 1 2 3 4 n ... U1 U2 U3 U4 Un ... Rumus Suku Ke-n
- 6. Contoh : 1. Diketahui barisan bilangan 4, 7, 12, 19, ... a. Tentukan rumus suku ke-n b. Suku keberapa dari barisan tersebut yang bernilai 199 2. Tentukan rumus suku ke-n dan Kemudian tentukan suku ke 20 dari barisan berikut. a. 3, 5, 7, 9, .... b. 3, 12, 37, 48, .... c. 1/4, 2/5, 3/6, 4/7, ... d. -3/9, 1/9, -1/27, 1/81, ... 3. Tentukan lima suku pertama dari barisan bilangan berikut. a. Un = 4n - 5 b. Un = 2 – n2 c. Un = (-1)n + 2n
- 7. Barisan dan Deret Aritmatika Barisan Aritmatika adalah suatu bilangan yang selisih setiap dua suku berurutan selalu merupakan bilangan tetap (konstan) A. Barisan Aritmatika Rumus : Un = a + (n – 1)b Keterangan : Un = Suku ke-n a = suku pertama b = beda n = banyak suku
- 8. Secara umum dapat dikatakan sebagai berikut Jika Un adalah suku ke-n dari suatu barisan aritmatika maka berlaku b = Un – Un-1 Contoh 1 : Tentukan suku ke-8 dan ke-20 dari barisan -3, 2, 7, 12, .... Jawab Suku Pertama adalah a = -3 dan Bedanya b = 2 – (-3) = 5 Dengan mensubstitusikan a dan b, diperoleh Un = -3 + (n - 1) 5 Suku ke-8 : U8 = -3 + (8 – 1) 5 = 32 Suku ke-20 : U20 = -3 + (20 – 1) 5 = 92
- 9. Contoh 2 : Suku ke-10 dan ke-14 dari barisan aritmatika berturut-turut adalah 7 dan 15. tentukan suku pertama, beda dan suku ke-20 barisan tersebut. Jawab Diketahui U10 = 7 dan U14 = 15, dari rumus suku ke-n barisan aritmatika Un = a + (n – 1)b, diperoleh 2 persamaan : U10 = 7  a + 9b = 7 …………………….(1) U14 = 15  a + 13b = 15 …………………….(2) Kita gunakan eliminasi dan substitusi, dari persamaan 1 dan 2 diperoleh :
- 10. a + 9b = 7 a + 13b = 15 – -4b = -8 b = 2 substitusikan b = 2 ke salah satu persamaan, misalnya persamaan (1) a + 9 (2) = 7  a = 7 – 18 a = -11 Diperoleh rumus suku ke-n adalah Un = -11 + (n -1)2 U20 = -11 + (20 – 1)2 = 27
- 11. SOAL 1. Carilah suku-suku yang diminta pada barisan berikut ini ! a. Suku ke-11 dari barisan -2, 3, 8, .... b. Suku ke-19 dari barisan 20, 17, 14, 11, ... c. Suku ke-21 dari barisan 1/5, 4/5, 7/5, 2, ... d. Suku ke-n dari barisan 6, 15, 24, ... 2. Pada suatu barisan aritmatika, diketahui suku ke-5 adalah 35 dan suku ke-9 adalah 43. tentukan suku ke-35 dan suku ke-100 3. Penomoran kursi paling pinggir di sebuah Gedung bioskop membentuk barisan aritmatika. Jika baris ke-4 bernomor 37 dan baris ke-10 bernomor 109. terletak di baris keberapakah nomor 313 ?
- 12. A. Barisan Aritmatika Deret Aritmatika adalah Jumlah seluruh suku-suku yang ada di barisan aritmatika Misalkan U1, U2, U3, …., Un merupakan suku-suku dari suatu barisan aritmatika Sn = U1 + U2 + U3 + … + Un disebut Deret Aritmatika Rumus umum jumlah n suku pertama deret aritmatika ( ) 2 n n n S a U     2 ( 1) 2 n n S a n b   ï€ atau
- 13. Contoh 1 : Tentukan jumlah 10 suku pertama dari deret 2 + 4 + 6 + 8 + .... Jawab Diketahui bahwa a = 2 b = 4 – 2 = 2 dan n = 10   2 ( 1) 2 n n S a n b   ï€ ï€¨  10 10 2.2 (10 1)2 2 S   ï€ ï€¨  5 4 18     5 22  110  Jadi jumlah 10 suku pertama dari deret 2+4+6+... adalah 110
- 14. Contoh 2 : Hitunglah jumlah semua bilangan asli kelipatan 3 yang kurang dari 50 Jawab Bilangan asli kelipatan 3 yang kurang dari 100 adalah 3, 6, 9, 12, … , 48 sehingga diperoleh a = 3, b = 3 dan Un = 48 Terlebih dahulu kita cari nilai n sebagai berikut Un = a + (n – 1)b 48 = 3 + (n – 1)3 48 = 3 + 3n – 3 3n = 48 n = 16
- 15. Jumlah dari 50 suku pertama deret tersebut   2 ( 1) 2 n n S a n b   ï€ ï€¨  16 16 2.3 (16 1)3 2 S   ï€ ï€¨  16 8 6 75 S     16 8 81 S  16 648 S  Jadi jumlah semua bilangan asli kelipatan 3 yang kurang dari 50 adalah 648
- 16. Soal 1. Hitunglah jumlah deret aritmatika berikut ini a. 1 + 4 + 7 + 10 + .... (20 suku) b. 96 + 93 + 90 + .... (10 suku) c. – 20 – 16 – 12 – 8 ... (30 suku) d. 1 + 3,5 + 6 + 8,5 + ... (12 suku) 2. Tentukan jumlah semua bilangan berikut ! a. Bilangan asli ganjil kurang dari 100 b. Bilangan asli kurang dari 85 yang habis dibagi 5 c. Bilangan kelipatan 4 antara 25 dan 200
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