1 / 11

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

graham
Download Presentation

Deret Aritmatika

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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!

More Related