Pertanyaan

Hitunglah U n dan S n pada deret geometri berikut: 3 2 , 9 4 , 27 8 , ... ( n = 10 )

Hitunglah $U_{n}$ dan $S_{n}$ pada deret geometri berikut:

$\frac{2}{3}$ , $\frac{4}{9}$ , $\frac{8}{27}$ , ... ( $n = 10$ )

P. Tessalonika

Master Teacher

Mahasiswa/Alumni Universitas Negeri Medan

Jawaban terverifikasi

Jawaban

nilai dan .

nilai $U subscript 10 equals fraction numerator 1.024 over denominator 59.049 end fraction$ dan $S subscript 10 equals fraction numerator 116.050 over denominator 59.049 end fraction$ .

Pembahasan

Diketahui: Ditanya: Jawab: Ingat bahwa rumus suku ke-n barisan geometri adalah , diperoleh: Ingat bahwa rumus jumlah 10 suku pertama deret geometri tersebut yaitu: Dengan demikian, nilai dan .

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row blank blank a end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 2 over 3 end cell end table

$table attributes columnalign right center left columnspacing 0px end attributes row r equals cell U subscript 2 over U subscript 1 end cell row blank equals cell 4 over 9 divided by 2 over 3 end cell row blank equals cell fraction numerator scriptbase up diagonal strike 4 end scriptbase presuperscript 2 over denominator scriptbase up diagonal strike 9 end scriptbase presuperscript 3 end fraction cross times fraction numerator up diagonal strike 3 over denominator up diagonal strike 2 end fraction end cell row blank equals cell 2 over 3 end cell end table$

Ditanya:

Jawab:

Ingat bahwa rumus suku ke-n barisan geometri adalah U subscript n equals a times r to the power of n minus 1 end exponent , diperoleh:

$table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 10 end cell equals cell a r to the power of 9 end cell row blank equals cell 2 over 3 times open parentheses 2 over 3 close parentheses to the power of 9 end cell row blank equals cell open parentheses 2 over 3 close parentheses to the power of 10 end cell row blank equals cell fraction numerator 1.024 over denominator 59.049 end fraction end cell end table$

Ingat bahwa rumus jumlah 10 suku pertama deret geometri tersebut yaitu:

$table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator a open parentheses 1 minus r to the power of n close parentheses over denominator 1 minus r end fraction end cell row cell S subscript 10 end cell equals cell fraction numerator begin display style 2 over 3 end style open parentheses 1 minus open parentheses begin display style 2 over 3 end style close parentheses to the power of 10 close parentheses over denominator 1 minus begin display style 2 over 3 end style end fraction end cell row blank equals cell fraction numerator begin display style 2 over 3 end style open parentheses 1 minus begin display style fraction numerator 1.024 over denominator 59.049 end fraction end style close parentheses over denominator begin display style 1 third end style end fraction end cell row blank equals cell fraction numerator 2. begin display style fraction numerator 58.025 over denominator 59.049 end fraction end style over denominator 1 end fraction end cell row blank equals cell fraction numerator 116.050 over denominator 59.049 end fraction end cell end table$

Dengan demikian, nilai $U subscript 10 equals fraction numerator 1.024 over denominator 59.049 end fraction$ dan $S subscript 10 equals fraction numerator 116.050 over denominator 59.049 end fraction$ .