Roboguru

Dalam deret geometri diketahui suku ke-2 dan suku ...

Dalam deret geometri diketahui suku ke-2begin mathsize 14px style equals 10 end style dan suku ke-5begin mathsize 14px style equals 80 end style. Suku ke-7 adalah undefined

  1. begin mathsize 14px style 300 end style

  2. begin mathsize 14px style 320 end style

  3. begin mathsize 14px style 280 end style

  4. begin mathsize 14px style 240 end style

  5. begin mathsize 14px style 160 end style

Jawaban:

Rumus baris geometri begin mathsize 14px style straight U subscript straight n equals straight U subscript 1 straight r to the power of straight n minus 1 end exponent end style.

Diketahui,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals 10 row cell straight U subscript 1 straight r to the power of 2 minus 1 end exponent end cell equals 10 row cell straight U subscript 1 straight r end cell equals 10 end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 5 end cell equals 80 row cell straight U subscript 1 straight r to the power of 5 minus 1 end exponent end cell equals 80 row cell straight U subscript 1 straight r to the power of 4 end cell equals 80 end table end style

Sehingga untuk mencari rasio sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator straight U subscript 1 straight r over denominator straight U subscript 1 straight r to the power of 4 end fraction end cell equals cell 10 over 80 end cell row cell straight r to the power of negative 3 end exponent end cell equals cell 1 over 8 end cell row cell straight r to the power of negative 3 end exponent end cell equals cell 2 to the power of negative 3 end exponent end cell row straight r equals 2 end table end style

Untuk mencari suku pertama begin mathsize 14px style open parentheses straight U subscript 1 close parentheses end style sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals 10 row cell straight U subscript 1 straight r end cell equals 10 row cell straight U subscript 1 open parentheses 2 close parentheses end cell equals 10 row cell straight U subscript 1 end cell equals cell 10 over 2 end cell row blank equals 5 end table end style

Maka, suku ke-7

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 U subscript 1 straight r to the power of 7 minus 1 end exponent end cell row blank equals cell 5 open parentheses 2 close parentheses to the power of 6 end cell row blank equals 320 end table end style

Jadi, jawaban yang tepat adalah B.

0

Ruangguru

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved