Dalam deret geometri, U7​=192 dan U2​=6, maka U9​=…

Pertanyaan

Dalam deret geometri, begin mathsize 14px style straight U subscript 7 equals 192 end style dan undefined, maka begin mathsize 14px style straight U subscript 9 equals horizontal ellipsis end style   

G. Albiah

Master Teacher

Mahasiswa/Alumni Universitas Galuh Ciamis

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 begin mathsize 14px style straight U subscript 9 equals 768 end style

Pembahasan

Diketahui deret geometri, 

  • begin mathsize 14px style straight U subscript 7 equals 192 end style dan undefined

Rumus suku kenegative n adalah Error converting from MathML to accessible text., maka

 table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 7 end cell equals cell ar to the power of 7 minus 1 end exponent end cell row blank equals cell ar to the power of 6 end cell row blank equals 192 end table 

 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals cell ar to the power of 2 minus 1 end exponent end cell row blank equals cell ar to the power of 1 end cell row blank equals ar row blank equals 6 end table

Jika kita bandingkan kedua suku tersebut didapat,

table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 7 over straight U subscript 2 end cell equals cell 192 over 6 end cell row cell fraction numerator up diagonal strike straight a straight r to the power of 6 over denominator up diagonal strike straight a straight r end fraction end cell equals cell 192 over 6 end cell row cell straight r to the power of 6 minus 1 end exponent end cell equals cell 192 over 6 end cell row cell straight r to the power of 5 end cell equals 32 row cell straight r to the power of 5 end cell equals cell fifth root of 32 end cell row cell straight r to the power of 5 end cell equals cell fifth root of 2 to the power of 5 end root end cell row straight r equals 2 end table  

Substitusikan ke salah satu suku sehingga,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals 6 row ar equals 6 row cell straight a cross times 2 end cell equals 6 row straight a equals 3 end table end style  

Maka, 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 9 end cell equals cell ar to the power of 9 minus 1 end exponent end cell row blank equals cell ar to the power of 8 end cell row blank equals cell 3 cross times 2 to the power of 8 end cell row blank equals cell 3 cross times 256 end cell row blank equals 768 end table          

Jadi, begin mathsize 14px style straight U subscript 9 equals 768 end style

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