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Suku ke dan suku ke suatu barisan geometri berturu...

Suku kebegin mathsize 14px style negative 4 end style dan suku kebegin mathsize 14px style negative 7 end style suatu barisan geometri berturut-turut begin mathsize 14px style 8 over 3 space text dan end text space 64 over 3 end style, jumlah begin mathsize 14px style 8 end style suku pertama deret tersebut ....

  1. 95space 

  2. 85space

  3. 81space

  4. 65space

Jawaban:

Rumus suku kebegin mathsize 14px style negative n end style dari barisan geometri  adalah

begin mathsize 14px style U subscript n equals a r to the power of n minus 1 end exponent end style.

Diketahui suku kebegin mathsize 14px style negative 4 end style suatu barisan geometri bernilai begin mathsize 14px style 8 over 3 end style maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 4 end cell equals cell 8 over 3 end cell row cell a r cubed end cell equals cell 8 over 3 end cell end table end style 

Suku kebegin mathsize 14px style negative 7 end style bernilai begin mathsize 14px style 64 over 3 end style maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 7 end cell equals cell 64 over 3 end cell row cell a r to the power of 6 end cell equals cell 64 over 3 end cell end table end style 

Perbandingan suku  kebegin mathsize 14px style negative 4 end style dan suku kebegin mathsize 14px style negative 7 end style adalah sebagai berikut,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 7 over U subscript 4 end cell equals cell fraction numerator a r to the power of 6 over denominator a r cubed end fraction equals fraction numerator begin display style bevelled 64 over 3 end style over denominator begin display style bevelled 8 over 3 end style end fraction end cell row cell r cubed end cell equals cell 64 over 8 equals 8 end cell row r equals cell cube root of 8 equals 2 end cell end table end style           begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 4 end cell equals cell a r cubed end cell row cell 8 over 3 end cell equals cell a times 2 cubed end cell row a equals cell fraction numerator 8 over denominator 3 times 2 cubed end fraction end cell row a equals cell 1 third end cell end table end style 

Didapatkan suku pertamanya begin mathsize 14px style 1 third end style dan rasionya begin mathsize 14px style 2 end style. Jumlah begin mathsize 14px style 8 end style suku pertama deret tersebut adalah,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator a open parentheses r to the power of n minus 1 close parentheses over denominator r minus 1 end fraction end cell row cell S subscript 8 end cell equals cell fraction numerator begin display style 1 third end style open parentheses 2 to the power of 8 minus 1 close parentheses over denominator 2 minus 1 end fraction end cell row cell S subscript 8 end cell equals cell 1 third open parentheses 255 close parentheses end cell row cell S subscript 8 end cell equals 85 end table end style 

Jadi, jawaban yang tepat adalah B.

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