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Pertanyaan

Jika a, b, c, d, dan e adalah bilangan real positif yang membentuk barisan aritmetika turun dan a, d, e membentuk barisan geometri, maka nilai straight b over straight e = .... 

  1. 7

  2. 6

  3. 5

  4. 4

  5. 3

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

Karena space straight a comma space straight b comma space straight c comma space straight d comma space straight e space membentuk space barisan space aritmatika space left parenthesis misal space dengan space beda space straight x right parenthesis comma  maka  straight b equals straight a plus straight x  straight c equals straight a plus 2 straight x  straight d equals straight a plus 3 straight x  straight e equals straight a plus 4 straight x    straight a comma space straight d comma space straight e space membentuk space barisan space geometri space maka  straight d over straight a equals straight e over straight d  straight d squared equals ae  open parentheses straight a plus 3 straight x close parentheses squared equals straight a open parentheses straight a plus 4 straight x close parentheses  straight a squared plus 6 ax plus 9 straight x squared equals straight a squared plus 4 ax  2 ax equals negative 9 straight x squared  box enclose straight a equals negative 9 over 2 straight x end enclose    Sehingga  straight b over straight e equals fraction numerator straight a plus straight x over denominator straight a plus 4 straight x end fraction  equals fraction numerator negative begin display style 9 over 2 end style straight x plus straight x over denominator negative begin display style 9 over 2 end style straight x plus 4 straight x end fraction  equals fraction numerator negative begin display style 7 over 2 end style straight x over denominator negative begin display style 1 half end style straight x end fraction  equals box enclose 7

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