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Pertanyaan

Suatu barisan geometri terdiri dari 10 suku. Jika jumlah suku-suku genap adalah 1.024 dan jumlah suku-suku ganjil adalah 512, maka jumlah 5 suku pertama barisan tersebut adalah ....

  1. begin mathsize 14px style fraction numerator 2.048 over denominator 11 end fraction end style 

  2. Error converting from MathML to accessible text. 

  3. size 14px 512 over size 14px 11 

  4. size 14px 256 over size 14px 11 

I. Roy

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah C.

Pembahasan

Diketahui terdapat 10 suku pada barisan tersebut dan jumlah suku-suku genap adalah 1.024 dan jumlah suku-suku ganjil adalah 824, maka kita punya

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 2 plus U subscript 4 plus U subscript 6 plus U subscript 8 plus U subscript 1 0 end cell equals cell 1.024 end cell row cell a r to the power of 2 minus 1 end exponent plus a r to the power of 4 minus 1 end exponent plus a r to the power of 6 minus 1 end exponent plus a r to the power of 8 minus 1 end exponent plus a r to the power of 10 minus 1 end exponent end cell equals cell 1.024 end cell row cell a r plus a r cubed plus a r to the power of 5 plus a r to the power of 7 plus a r to the power of 9 end cell equals cell 1.024 end cell row cell a r left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end cell equals cell 1.024 end cell row blank blank blank row cell U subscript 1 plus U subscript 3 plus U subscript 5 plus U subscript 7 plus U subscript 9 end cell equals 512 row cell a plus a r to the power of 3 minus 1 end exponent plus a r to the power of 5 minus 1 end exponent plus a r to the power of 7 minus 1 end exponent plus a r to the power of 9 minus 1 end exponent end cell equals 512 row cell a plus a r squared plus a r to the power of 4 plus a r to the power of 6 plus a r to the power of 8 end cell equals 512 row cell a left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end cell equals 512 end table end style 

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator a r left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis over denominator a left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end fraction end cell equals cell fraction numerator 1.024 over denominator 512 end fraction end cell row cell fraction numerator a r up diagonal strike left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end strike over denominator a up diagonal strike left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end strike end fraction end cell equals cell fraction numerator 1.024 over denominator 512 end fraction end cell row cell fraction numerator a r over denominator a end fraction end cell equals cell fraction numerator 1.024 over denominator 512 end fraction end cell row r equals 2 end table end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a left parenthesis 1 plus r squared plus r to the power of 4 plus r to the power of 6 plus r to the power of 8 right parenthesis end cell equals 512 row cell a left parenthesis 1 plus 2 squared plus 2 to the power of 4 plus 2 to the power of 6 plus 2 to the power of 8 right parenthesis end cell equals 512 row cell a left parenthesis 1 plus 4 plus 16 plus 64 plus 256 right parenthesis end cell equals 512 row cell a left parenthesis 341 right parenthesis end cell equals 512 row a equals cell 512 over 341 end cell end table end style 

Dengan demikian, jumlah 5 suku pertama 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 left parenthesis r to the power of n minus 1 right parenthesis over denominator r minus 1 end fraction end cell row cell S subscript 5 end cell equals cell fraction numerator begin display style 512 over 341 end style left parenthesis 2 to the power of 5 minus 1 right parenthesis over denominator 2 minus 1 end fraction end cell row blank equals cell fraction numerator begin display style 512 over 341 left parenthesis 32 minus 1 right parenthesis end style over denominator 1 end fraction end cell row blank equals cell 512 over 341 left parenthesis 31 right parenthesis end cell row blank equals cell 512 over 11 end cell end table end style 

Jadi, jawaban yang tepat adalah C.

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