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Diketahui barisan bilangan 32, 16, 8, 4, ... . Rumus suku ke-n adalah ....

Pertanyaan

Diketahui barisan bilangan 32, 16, 8, 4, ... . Rumus suku ke-n adalah ....

  1. 2 to the power of 6 plus n end exponent

  2. 2 to the power of 5 plus n end exponent

  3. 2 to the power of 6 minus n end exponent

  4. 2 to the power of 5 minus n end exponent

Pembahasan Soal:

Barisan space pada space soal space termasuk space barisan space geometri space dengan space straight a equals 32 equals 2 to the power of 5 comma space straight r equals 16 over 32 equals 1 half equals 2 to the power of negative 1 end exponent  straight U subscript straight n space equals space ar to the power of straight n minus 1 end exponent  straight U subscript straight n space equals space 2 to the power of 5 left parenthesis 2 to the power of negative 1 end exponent right parenthesis to the power of n minus 1 end exponent  straight U subscript straight n space equals space 2 to the power of 5 2 to the power of negative n plus 1 end exponent  straight U subscript straight n space equals space 2 to the power of 5 minus n plus 1 end exponent  straight U subscript straight n space equals space 2 to the power of 6 minus n end exponent

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Rizky

Mahasiswa/Alumni Universitas Negeri Malang

Terakhir diupdate 14 Desember 2020

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Pertanyaan yang serupa

Rumus suku ke-n dari barisan bilangan 9,3,1,31​,... adalah ...

Pembahasan Soal:

Ingat rasio deret geometri:

r equals U subscript 2 over U subscript 1 equals U subscript 3 over U subscript 2

Maka:

r equals U subscript 2 over U subscript 1 equals 3 over 9 equals 1 third

Suku ke-n deret geometri adalah

U subscript n equals a r to the power of n minus 1 end exponent

Maka:

U subscript n equals 9 open parentheses 1 third close parentheses to the power of n minus 1 end exponent  equals open parentheses 3 squared close parentheses open parentheses 3 to the power of negative 1 end exponent close parentheses to the power of n minus 1 end exponent  equals 3 squared.3 to the power of 1 minus n end exponent  equals 3 to the power of 2 plus 1 minus n end exponent  equals 3 to the power of 3 minus n end exponent

1

Roboguru

Diketahui barisan bilangan 32, 16, 8, 4, .... Rumus suku ke-n adalah ....

Pembahasan Soal:

Perhatikan space polanya comma space maka colon  U subscript 1 space equals space a space equals space 32  U subscript 2 space equals space 16  U subscript 3 space equals space 8  terlihat space bahwa space barisan space tersebut space berupa space barisan space geometri  r equals U subscript 2 over U subscript 1 space left right arrow space r space equals space 16 over 32 space equals space 1 half  sehingga colon  U subscript n space equals space a. r to the power of n minus 1 end exponent  space space space space space space space space equals space 32. open parentheses 1 half close parentheses to the power of n minus 1 end exponent  space space space space space space space space equals space 2 to the power of 5 left parenthesis 2 to the power of negative 1 end exponent right parenthesis to the power of n minus 1 end exponent  space space space space space space space space equals space 2 to the power of 5 minus n plus 1 end exponent space  space space space space space space space space equals space 2 to the power of 6 minus n end exponent

0

Roboguru

Suatu deret geometri suku kedua sama dengan 2 dan suku kelima sama dengan 2716​. Tentukan rumus jumlah n suku pertamanya!

Pembahasan Soal:

Diketahui:

Suku kedua sama dengan 2, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell a r to the power of 2 minus 1 end exponent end cell equals 2 row cell a r end cell equals 2 end table

Suku kelima sama dengan 16 over 27, maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell a r to the power of 5 minus 1 end exponent end cell equals cell 16 over 27 end cell row cell a r to the power of 4 end cell equals cell 16 over 27 end cell end table

Sehingga diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell a r to the power of 4 end cell equals cell 16 over 27 end cell row cell a r times r cubed end cell equals cell 16 over 27 end cell row cell 2 times r cubed end cell equals cell 16 over 27 end cell row cell r cubed end cell equals cell fraction numerator 16 over denominator 2 times 27 end fraction end cell row cell r cubed end cell equals cell 16 over 54 end cell row cell r cubed end cell equals cell 8 over 27 end cell row r equals cell cube root of 8 over 27 end root end cell row r equals cell 2 over 3 end cell end table

Substitusi r equals 2 over 3 ke suku ke dua deret geometri.

table attributes columnalign right center left columnspacing 0px end attributes row cell a r end cell equals 2 row cell a open parentheses 2 over 3 close parentheses end cell equals 2 row cell 2 a end cell equals 6 row a equals cell 6 over 2 end cell row a equals 3 end table

Dengan menggunakan rumus jumah suku ke n, diperoleh:

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 comma space r not equal to 1 space dan space r less than 1 end cell row cell S subscript n end cell equals cell fraction numerator 3 open parentheses 1 minus open parentheses begin display style 2 over 3 end style close parentheses to the power of n close parentheses over denominator 1 minus begin display style 2 over 3 end style end fraction end cell row cell S subscript n end cell equals cell fraction numerator 3 open parentheses 1 minus open parentheses begin display style 2 over 3 end style close parentheses to the power of n close parentheses over denominator begin display style 3 over 3 end style minus begin display style 2 over 3 end style end fraction end cell row cell S subscript n end cell equals cell fraction numerator 3 open parentheses 1 minus open parentheses begin display style 2 over 3 end style close parentheses to the power of n close parentheses over denominator begin display style 1 third end style end fraction end cell row cell S subscript n end cell equals cell 3 open parentheses 1 minus open parentheses 2 over 3 close parentheses to the power of n close parentheses times 3 over 1 end cell row cell S subscript n end cell equals cell 9 open parentheses 1 minus open parentheses 2 over 3 close parentheses to the power of n close parentheses end cell end table

Maka, rumus jumlah n suku pertamanya adalah S subscript n equals 9 open parentheses 1 minus open parentheses 2 over 3 close parentheses to the power of n close parentheses.

0

Roboguru

Rumus suku ke-n pada barisan geometri 384, 192, 81, … adalah

Pembahasan Soal:

Barisan geometri 384, 192, 81, undefined mempunyai a = 384 dan r = begin mathsize 14px style 1 half end style.

Rumus suku ke-n

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript straight n end cell equals cell straight a cross times straight r to the power of straight n minus 1 end exponent end cell row cell straight U subscript straight n end cell equals cell 384 cross times open parentheses 1 half close parentheses to the power of straight n minus 1 end exponent end cell end table end style  

0

Roboguru

Suku kedua dan suku kelima dari suatu barisan geometri berturut-turut adalah 45 dan 35​. Suku ke-7 barisan tersebut adalah …

Pembahasan Soal:

begin mathsize 14px style straight U subscript straight n equals straight a times straight r to the power of straight n minus 1 end exponent straight U subscript 2 equals 45 left right double arrow straight a times straight r equals 45 space midline horizontal ellipsis space left parenthesis 1 right parenthesis straight U subscript 5 equals 5 over 3 left right double arrow straight a times straight r to the power of 4 equals 5 over 3 space midline horizontal ellipsis space left parenthesis 2 right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 5 over straight U subscript 2 end cell equals cell fraction numerator begin display style 5 over 3 end style over denominator 45 end fraction end cell row cell fraction numerator up diagonal strike straight a times straight r to the power of 4 over denominator up diagonal strike straight a times straight r end fraction end cell equals cell 5 over 3 cross times 1 over 45 end cell row cell straight r cubed end cell equals cell 1 over 27 end cell row straight r equals cell 1 third end cell row blank blank blank end table end style

Substitusi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals 45 row cell straight a times straight r end cell equals 45 row cell straight a times 1 third end cell equals 45 row straight a equals 135 end table end style

Sehingga, suku ke-7 adalah

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 7 end cell equals cell straight a times straight r to the power of 6 end cell row cell straight U subscript 7 end cell equals cell 135 times open parentheses 1 third close parentheses to the power of 6 end cell row cell straight U subscript 7 end cell equals cell 135 times 1 over 729 end cell row cell straight U subscript 7 end cell equals cell 5 over 27 end cell row blank blank blank end table end style 

0

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