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Diketahui suku pertama deret geometri adalah 4 m ​ dengan m > 0 dan suku ke-7 adalah m 3 . Jika rasio deret geometri tersebut positif, maka suku ke-19 adalah ....

Diketahui suku pertama deret geometri adalah  dengan > 0 dan suku ke-7 adalah . Jika rasio deret geometri tersebut positif, maka suku ke-19 adalah ....

  1. Error converting from MathML to accessible text. 

  2. begin mathsize 14px style straight m to the power of 7 space fourth root of straight m end style 

  3. begin mathsize 14px style straight m to the power of 8 space square root of straight m end style

  4. begin mathsize 14px style straight m to the power of 8 space fourth root of straight m end style 

  5. begin mathsize 14px style straight m to the power of 9 space square root of straight m end style 

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

jawaban yang tepat adalah C.

Pembahasan

Diketahui bahwa terdapat barisan geometri dengan Ingat bahwa pada barisan geometri berlaku Sehigga Pada soal diketahui bahwa rasionya positif, maka Sehingga suku ke-19 yaitu Jadi, jawaban yang tepat adalah C.

Diketahui bahwa terdapat barisan geometri dengan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight a equals cell fourth root of straight m equals straight m to the power of 1 fourth end exponent end cell row cell straight U subscript 7 end cell equals cell straight m cubed end cell end table end style

Ingat bahwa pada barisan geometri berlaku

begin mathsize 14px style straight U subscript straight n equals ar to the power of straight n minus 1 end exponent end style 

Sehigga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 7 end cell equals cell straight m cubed end cell row cell ar to the power of 7 minus 1 end exponent end cell equals cell straight m cubed end cell row cell straight m to the power of 1 fourth end exponent straight r to the power of 6 end cell equals cell straight m cubed end cell row cell straight r to the power of 6 end cell equals cell straight m cubed over straight m to the power of 1 fourth end exponent end cell row cell straight r to the power of 6 end cell equals cell straight m to the power of 3 minus 1 fourth end exponent end cell row cell straight r to the power of 6 end cell equals cell straight m to the power of 11 over 4 end exponent end cell row straight r equals cell plus-or-minus root index 6 of straight m to the power of 11 over 4 end exponent end root end cell row blank blank blank end table end style

Pada soal diketahui bahwa rasionya positif, maka

begin mathsize 14px style straight r equals root index 6 of straight m to the power of 11 over 4 end exponent end root straight r equals open parentheses straight m to the power of 11 over 4 end exponent close parentheses to the power of 1 over 6 end exponent straight r equals straight m to the power of 11 over 24 end exponent end style 

Sehingga suku ke-19 yaitu

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 19 end cell equals cell ar to the power of 19 minus 1 end exponent end cell row blank equals cell ar to the power of 18 end cell row blank equals cell straight m to the power of 1 fourth end exponent open parentheses straight m to the power of 11 over 24 end exponent close parentheses to the power of 18 end cell row blank equals cell straight m to the power of 1 fourth end exponent straight m to the power of open parentheses 11 over 24 close parentheses space. space 18 end exponent end cell row blank equals cell straight m to the power of 1 fourth end exponent straight m to the power of open parentheses 11 over 4 close parentheses space. space 3 end exponent end cell row blank equals cell straight m to the power of 1 fourth end exponent straight m to the power of 33 over 4 end exponent end cell row blank equals cell straight m to the power of 1 fourth plus end exponent to the power of 33 over 4 end exponent end cell row blank equals cell straight m to the power of 34 over 4 end exponent end cell row blank equals cell straight m to the power of 17 over 2 end exponent end cell row blank equals cell straight m to the power of 16 over 2 plus 1 half end exponent end cell row blank equals cell straight m to the power of 16 over 2 end exponent space. space straight m to the power of 1 half end exponent end cell row blank equals cell straight m to the power of 8 square root of straight m end cell end table end style 

Jadi, jawaban yang tepat adalah C.

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Dalam suatu barisan geometri, U 1 ​ + U 3 ​ + U 5 ​ = s dan U 2 ​ + U 4 ​ + U 6 ​ = t . Maka U 3 ​ adalah ....

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