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Suku ke-2 dan suku ke-5 suatu deret geometri bertu...

Suku ke-2 dan suku ke-5 suatu deret geometri berturut-turut adalah 8 dan 1. Jumlah lima suku pertama adalah ....

  1. 28

  2. 30

  3. 31

  4. begin mathsize 12px style 31 1 half end style

  5. begin mathsize 12px style 31 3 over 4 end style

Jawaban:

begin mathsize 12px style straight U subscript 2 equals ar to the power of 2 minus 1 end exponent  8 equals ar  straight U subscript 5 equals ar to the power of 5 minus 1 end exponent  1 equals ar to the power of 4 end style

Dengan membandingkan U5 dan U2

begin mathsize 12px style straight U subscript 5 over straight U subscript 2 equals ar to the power of 4 over ar  1 over 8 equals straight r cubed  1 over 8 equals straight r cubed  straight r equals 1 half end style

Substitusi nilai r ke dalam U2

begin mathsize 12px style straight U subscript 2 equals ar  8 equals straight a open parentheses 1 half close parentheses  straight a equals 16  Rumus space straight S subscript straight n  straight S subscript straight n equals fraction numerator straight a left parenthesis straight r to the power of straight n minus 1 right parenthesis over denominator straight r minus 1 end fraction end style

Jadi, Jumlah lima suku pertama :

begin mathsize 12px style straight S subscript 5 equals fraction numerator 16 open parentheses begin display style 1 half to the power of 5 minus 1 end style close parentheses over denominator begin display style 1 half minus 1 end style end fraction  straight S subscript 5 equals fraction numerator 16 open parentheses begin display style 1 over 32 minus 1 end style close parentheses over denominator begin display style negative 1 half end style end fraction  straight S subscript 5 equals 32 open parentheses 31 over 32 close parentheses  straight S subscript 5 equals 31 end style

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