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Suatu barisan geometri memiliki suku ke-4 = 5 dan ...

Suatu barisan geometri memiliki suku ke-4 = 5 dan suku ke-5 =begin mathsize 12px style 1 fifth end style. Suku ke-2 adalah ....

  1. 630

  2. 475

  3. 225

  4. 175

  5. 125

Jawaban:

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straight U subscript 5 over straight U subscript 4 equals ar to the power of 4 over ar cubed  fraction numerator begin display style 1 fifth end style over denominator 5 end fraction equals straight r  1 over 25 equals straight r  straight r equals 5 to the power of negative 2 end exponent  Substitusikan space straight r space ke space salah space satu space persamaan space sehingga space colon

straight U subscript 5 equals ar to the power of 5 minus 1 end exponent  1 fifth equals straight a open parentheses 5 to the power of negative 2 end exponent close parentheses to the power of 4  1 fifth equals straight a 5 to the power of negative 8 end exponent  5 to the power of 7 equals straight a    Maka space straight U subscript 2 equals ar to the power of 2 minus 1 end exponent  space space space space space space space space space space straight U squared equals ar to the power of 1  space space space space space space space space space space straight U subscript 2 equals open parentheses 5 to the power of 7 close parentheses open parentheses 5 to the power of negative 2 end exponent close parentheses  space space space space space space space space space space straight U subscript 2 equals 5 to the power of 5  space space space space space space space space space space straight U subscript 2 equals 3.125

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