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Pertanyaan

Diketahui deret geometri mempunyai suku ke-2 = 6 dan suku ke-4 = 3 over 2. Jumlah 6 suku pertamanya adalah ...

  1. 192 over 8

  2. 189 over 8

  3. 165 over 8

  4. 146 over 8

  5. 123 over 6

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Geometri

U subscript n equals a r to the power of n minus 1 end exponent  S subscript n equals fraction numerator a left parenthesis r to the power of n minus 1 end exponent right parenthesis over denominator r minus 1 end fraction

Maka

U subscript 2 equals a r to the power of 2 minus 1 end exponent rightwards arrow 6 equals a r  U subscript 4 equals a r to the power of 4 minus 1 end exponent rightwards arrow 3 over 2 equals a r cubed  fraction numerator a r cubed over denominator a r end fraction equals fraction numerator begin display style 3 over 2 end style over denominator 6 end fraction  r squared equals 1 fourth  r equals plus-or-minus 1 half

Untuk r = 1 half

a r equals 6 rightwards arrow a open parentheses 1 half close parentheses equals 6 rightwards arrow a equals 12  S subscript n equals fraction numerator 12 open parentheses open parentheses begin display style 1 half end style close parentheses to the power of 6 minus 1 close parentheses over denominator begin display style 1 half end style minus 1 end fraction equals fraction numerator 12 open parentheses begin display style 1 over 64 end style minus 1 close parentheses over denominator negative begin display style 1 half end style end fraction equals fraction numerator negative begin display style 189 over 16 end style over denominator negative begin display style 1 half end style end fraction equals 189 over 8

Untuk r = negative 1 half

a r equals 6 rightwards arrow a open parentheses 1 half close parentheses equals 6 rightwards arrow a equals 12  S subscript n equals fraction numerator 12 open parentheses open parentheses begin display style negative 1 half end style close parentheses to the power of 6 minus 1 close parentheses over denominator negative begin display style 1 half end style minus 1 end fraction equals fraction numerator negative 12 open parentheses begin display style 1 over 64 end style minus 1 close parentheses over denominator negative begin display style 3 over 2 end style end fraction equals 8 open parentheses negative 63 over 64 close parentheses equals negative 63 over 8

Jawaban yang sesuai pilihan ganda adalah B

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Hitunglah jumlah 7 suku pertama deret geometri 31​+91​+271​+… .

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