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Deret Aritmatika

Deret Aritmatika. Dian Ayu Prastiwi Angger Isyuanita Dian Rizky Nurul Fibia Adimas Pandu Hanif Bustani Adil Wirawan Muhammad Al Fatih. Slide Menu. Definisi , Penjelasan & Contoh Soal Soal – Soal Sumber Penutup. Deret Aritmatika. Definisi

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Deret Aritmatika

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  1. Deret Aritmatika Dian Ayu PrastiwiAngger Isyuanita Dian RizkyNurulFibia AdimasPandu HanifBustani AdilWirawan Muhammad Al Fatih

  2. Slide Menu • Definisi, Penjelasan & ContohSoal • Soal– Soal • Sumber • Penutup

  3. Deret Aritmatika • Definisi • Deretaritmetikaadalahjumlahn sukupertamabarisanaritmetika. Jumlahn sukupertamadarisuatubarisanbilangandinotasikanSn. Dengandemikian, Sn= U1 + U2 + U3 + ... + Un MisalkanU1, U2, U3, ..., Un merupakansuku-sukudarisuatubarisanaritmatika. U1 + U2 + U3 + ... + Un disebutderetaritmatika, denganUn = a + (n – 1)b.

  4. … • Olehkarena U1 = a, U2 = a+b, U3 = a+2b, … , U(n-2) = Un-2b dan U(n-1) = Un-b maka : Sn = a + (a+b) + (a+2b) + ... + (Un-2b) + (Un-b) + Un Sn = Un + (Un – b) + (Un – 2b) + ... + (a+2b) + (a+b) + a 2Sn = (a + Un ) + (a + Un )+ (a + Un ) + ... + (a + Un )

  5. Penjumlahan Sebanyak n Suku 2Sn = (a + Un ) + (a + Un )+ (a + Un ) + ... + (a + Un ) maka 2Sn = n(a + Un) Sn = n(a + Un) , olehkarenaUn = a + (n-1)b, maka Sn = n[a + (a + (n – 1)b)] Sn = n[2a + (n – 1)b]

  6. Contoh 1 : Diketahuisuatubarisanaritmatika 2, 5, 8, 11, 14. Tentukanjumlahkelimasukubarisantersebut. Jawab: Jumlahkelimasuku 2, 5, 8, 11, 14 dapatdituliskansebagaiberikut. S5= 2 + 5 + 8 + 11 + 14 S5= 14 + 11 + 8 + 5 + 2 2S5 = 16 + 16 + 16 + 16 + 16 2S5= 5 x 16 S5 = S5 = 40 Jadi, jumlahkelimasukubarisantersebutadalah 40.

  7. Contoh 2 Carilahjumlah 100 sukupertamadarideret 2 + 4 + 6 + 8 +.... Jawab: Diketahuibahwaa = 2, b = 4 – 2 = 2, dann = 100. S100 = x 100 [2(2) + (100 – 1)2] = 50 [4 + 198] = 50 (202) = 10.100 Jadi, jumlah 100 sukupertamadariderettersebutadalah 10.100. Kembali

  8. Sumber • Nehemiah. 2003. Matematika 3. BalaiPustaka. • Dr. Ir. Bob Foster, M.M. 2011. Koding. Ganesha Operation. Kembali

  9. Soal 1. Diketahuideretaritmatikadengan U3 = 11 dan U7 = 27 Tentukan : a. SukuPertama b. U10 c. S10 2. Jumlah n sukupertamaderetaritmatikaadalah Sn = n + n Beda darideretaritmatikatersebutadalah…

  10. Soal 3. Nilaidari + adalah… 4. Snadalahjumlah n sukupertamaderetaritmatika. Jika a adalahsukupertamadan b bedaderetitu, makanilai S(n+2) – Snadalah… 5. log a + log (ab) + log (ab ) +log (ab ) + … adalahderetaritmatika. Makajumlah 6 sukupertamaadalah.. Kembali

  11. Terima Kasih Atas Perhatiannya SelamatBelajar!

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