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Jika -2, a+3, a-1 membentuk barisan geometri, maka jumlah 11 suku pertama yang mungkin adalah ....

Jika -2, a+3, a-1 membentuk barisan geometri, maka jumlah 11 suku pertama yang mungkin adalah ....

  1. -2

  2. -1

  3. 0

  4. 1

  5. 2

Jawaban:

Ingat space bahwa space pada space barisan space geometri space berlaku  straight r equals straight u subscript 2 over straight u subscript 1 equals straight u subscript 3 over straight u subscript 2  Maka  fraction numerator straight a plus 3 over denominator negative 2 end fraction equals fraction numerator straight a minus 1 over denominator straight a plus 3 end fraction  left parenthesis straight a plus 3 right parenthesis squared equals negative 2 left parenthesis straight a minus 1 right parenthesis  straight a squared plus 6 straight a plus 9 equals negative 2 straight a plus 2  straight a squared plus 8 straight a plus 7 equals 0  left parenthesis straight a plus 1 right parenthesis left parenthesis straight a plus 7 right parenthesis equals 0  Sehingga  straight a plus 1 equals 0 rightwards arrow box enclose straight a equals negative 1 end enclose  straight a plus 7 equals 0 rightwards arrow box enclose straight a equals negative 7 end enclose    Jika space straight a equals negative 1 comma space maka  straight r equals fraction numerator straight a plus 3 over denominator negative 2 end fraction equals fraction numerator negative 1 plus 3 over denominator negative 2 end fraction equals fraction numerator 2 over denominator negative 2 end fraction equals box enclose negative 1 end enclose    Jika space straight a equals negative 7 comma space maka  straight r equals fraction numerator straight a plus 3 over denominator negative 2 end fraction equals fraction numerator negative 7 plus 3 over denominator negative 2 end fraction equals fraction numerator negative 4 over denominator negative 2 end fraction equals box enclose 2    Jika space straight r equals negative 1 comma space maka  straight S subscript 11 equals fraction numerator negative 2 open parentheses open parentheses negative 1 close parentheses to the power of 11 minus 1 close parentheses over denominator open parentheses negative 1 close parentheses minus 1 end fraction equals fraction numerator negative 2 open parentheses negative 1 minus 1 close parentheses over denominator negative 1 minus 1 end fraction equals fraction numerator negative 2 open parentheses negative 2 close parentheses over denominator negative 2 end fraction equals box enclose negative 2 end enclose  Jika space straight r equals negative 7 comma space maka  straight S subscript 11 equals fraction numerator negative 2 open parentheses 2 to the power of 11 minus 1 close parentheses over denominator 2 minus 1 end fraction equals fraction numerator negative 2 open parentheses 2048 minus 1 close parentheses over denominator 1 end fraction equals negative 2 open parentheses 2047 close parentheses equals box enclose negative 4094 end enclose

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