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Jika a n ​ merupakan suku ke- n dari suatu barisan aritmetika, a 1 ​ + a 2 ​ + a 3 ​ − 9 = 0 ,dan a 3 ​ + a 4 ​ + a 5 ​ = 15 ,tentukanlah: a 1 ​ + a 2 ​ + a 3 ​ + a 4 ​ + a 5 ​ .

Jika  merupakan suku ke- dari suatu barisan aritmetika, , dan , tentukanlah: 

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M. Nasrullah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

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Pembahasan

Kita eliminasi persamaan 1 dan 2 = subtitusi nilai kedalam persamaan 1

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a subscript 1 plus a subscript 2 plus a subscript 3 minus 9 end cell equals 0 row cell a subscript 1 plus a subscript 2 plus a subscript 3 end cell equals cell negative 9 end cell row cell a plus a plus b plus a plus 2 b end cell equals 9 row cell 3 a plus 3 b end cell equals 9 row cell a plus b end cell equals cell 3... left parenthesis 1 right parenthesis end cell end table end style 

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px a subscript size 14px 3 size 14px plus size 14px a subscript size 14px 4 size 14px plus size 14px a subscript size 14px 5 end cell size 14px equals cell size 14px 15 size 14px space end cell row cell size 14px a size 14px plus size 14px 2 size 14px b size 14px plus size 14px a size 14px plus size 14px 3 size 14px b size 14px plus size 14px a size 14px plus size 14px 4 size 14px b end cell size 14px equals size 14px 15 row cell size 14px 3 size 14px a size 14px plus size 14px 9 size 14px b end cell size 14px equals size 14px 15 row cell size 14px a size 14px plus size 14px 3 size 14px b end cell size 14px equals cell size 14px 5 size 14px. size 14px. size 14px. size 14px left parenthesis size 14px 2 size 14px right parenthesis end cell end table

Kita eliminasi persamaan 1 dan 2

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell b minus 3 b end cell equals cell 3 minus 5 end cell row cell negative 2 b end cell equals cell negative 2 end cell row b equals 1 end table end style =

subtitusi nilai begin mathsize 14px style b equals 1 end style kedalam persamaan 1

begin mathsize 14px style a plus 3 open parentheses 1 close parentheses equals 5 a equals 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a subscript 1 plus a subscript 2 plus a subscript 3 plus a subscript 4 plus a subscript 5 end cell equals cell S subscript 5 end cell row blank equals cell 5 over 2 left parenthesis 2 open parentheses 2 close parentheses plus 4 open parentheses 1 close parentheses right parenthesis end cell row blank equals cell 5 over 2 left parenthesis 8 right parenthesis end cell row blank equals 20 end table end style

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Tentukan jumlah dari setiap deret aritmetika berikut ini. a. 3 π ​ + 3 2 π ​ + π + 3 4 π ​ + ... + 3 13 π ​

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