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jika suku ke-3 barisan geometri adalah dan suku ke-6 adalah , maka suku ke-9 adalah ...

jika suku ke-3 barisan geometri adalah begin mathsize 14px style square root of a end style dan suku ke-6 adalah begin mathsize 14px style a square root of a end style, maka suku ke-9 adalah ... 

  1. begin mathsize 14px style a squared square root of a end style 

  2. begin mathsize 14px style a squared cube root of a end style 

  3. begin mathsize 14px style a squared root index 6 of a end style 

  4. begin mathsize 14px style a cubed end style 

  5. begin mathsize 14px style a to the power of 4 end style 

Jawaban:

Berdasarkan informasi soal, diperoleh

begin mathsize 14px style U subscript 3 equals square root of a U subscript 6 equals a square root of a end style

pertama, kita cari terlebih dahulu nilai dengan membagi kedua persamaan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 3 over U subscript 6 end cell equals cell fraction numerator square root of a over denominator a square root of a end fraction end cell row cell fraction numerator U subscript 1 r squared over denominator U subscript 1 r to the power of 5 end fraction end cell equals cell 1 over a end cell row cell 1 over r cubed end cell equals cell 1 over a end cell row cell r cubed end cell equals a row r equals cell cube root of a end cell row blank blank blank end table end style 

kemudian kita cari suku pertama 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 3 end cell equals cell square root of a end cell row cell U subscript 1 r squared end cell equals cell square root of a end cell row cell U subscript 1 open parentheses cube root of a close parentheses squared end cell equals cell square root of a end cell row cell U subscript 1 end cell equals cell a to the power of begin display style 1 half end style end exponent over a to the power of begin display style 2 over 3 end style end exponent end cell row cell U subscript 1 end cell equals cell a to the power of 1 half minus 2 over 3 end exponent end cell row blank equals cell a to the power of negative 1 over 6 end exponent end cell row blank equals cell fraction numerator 1 over denominator root index 6 of a end fraction end cell end table end style

selanjutnya mencari suku ke-9

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 9 end cell equals cell U subscript 1 r to the power of 8 end cell row blank equals cell fraction numerator 1 over denominator root index 6 of a end fraction cross times open parentheses cube root of a close parentheses to the power of 8 end cell row blank equals cell a to the power of begin display style 8 over 3 end style end exponent over a to the power of begin display style 1 over 6 end style end exponent end cell row cell U subscript 9 end cell equals cell a to the power of 8 over 3 minus 1 over 6 end exponent end cell row blank equals cell a to the power of 15 over 6 end exponent end cell row blank equals cell a to the power of 5 over 2 end exponent end cell row blank equals cell a squared square root of a end cell end table end style

Jadi, jawaban yang tepat adalah A.

 

 

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