Roboguru

Pada suatu deret aritmatika diketahui . Jika nilai  maka jumlah 10 suku pertamanya adalah ....

Pertanyaan

Pada suatu deret aritmatika diketahui begin mathsize 14px style U subscript 5 plus U subscript 7 plus U subscript 9 plus U subscript 11 plus... plus U subscript 19 equals 112 end style. Jika nilai begin mathsize 14px style U subscript 9 equals 8 end style maka jumlah 10 suku pertamanya adalah ....

  1. 5undefined 

  2. 7undefined 

  3. 8undefined 

  4. 10undefined 

  5. 12undefined 

Pembahasan Video:

Pembahasan Soal:

Diketahui:

begin mathsize 14px style U subscript 5 plus U subscript 7 plus U subscript 9 plus U subscript 11 plus... plus U subscript 19 equals 112 end style 

begin mathsize 14px style U subscript 9 equals 8 end style

Ditanya: begin mathsize 14px style S subscript 10 equals... end subscript end style?

Jawab:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 5 plus U subscript 7 plus U subscript 9 plus U subscript 11 plus... plus U subscript 19 end cell equals 112 row cell a plus 4 b plus a plus 6 b plus a plus 8 b plus... plus a plus 18 b end cell equals 112 row cell 8 a plus 88 b end cell equals 112 row cell a plus 11 b end cell equals cell 14.... left parenthesis p e r s space 1 right parenthesis end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 9 end cell equals 8 row cell a plus 8 b end cell equals cell 8.... left parenthesis P e r s space 2 right parenthesis end cell end table end style

Eliminasi Pers 1 dan 2

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell stack attributes charalign center stackalign right end attributes row a plus 11 b equals 14 none end row row a plus 8 b equals 8 none minus end row horizontal line row 3 b equals 6 end row row b equals 6 over 3 end row row b equals 2 end row end stack end cell row blank blank blank row blank blank blank end table end style

Substitusi nilai b

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a plus 8 open parentheses 2 close parentheses end cell equals 8 row cell a plus 16 end cell equals 8 row a equals cell 8 minus 16 end cell row blank equals cell negative 8 end cell end table end style

 

Rumus begin mathsize 14px style S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript 10 end cell equals cell 10 over 2 left parenthesis 2 left parenthesis negative 8 right parenthesis plus 9 times 2 right parenthesis end cell row blank equals cell 5 left parenthesis negative 16 plus 18 right parenthesis end cell row blank equals cell 5 left parenthesis 2 right parenthesis end cell row blank equals 10 end table end style

 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Mei 2021

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