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Pertanyaan

Jumlah lima suku pertama deret aritmetika adalah negative 5 dan suku ke enam adalah negative 10. Jumlah 17 suku pertama deret tersebut adalah ...

  1. negative 475 

  2. negative 418 

  3. negative 369 

  4. negative 323 

  5. negative 280 

D. Rajib

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Diketahui :

jumlah space 5 space suku space pertama space left parenthesis straight S subscript 5 right parenthesis equals negative 5 suku space keenam space left parenthesis straight U subscript 6 right parenthesis equals negative 10  

Ingat kembali bahwa 

straight S subscript straight n equals straight n over 2 left parenthesis straight a plus straight U subscript straight n right parenthesis straight U subscript straight n equals straight a plus left parenthesis straight n minus 1 right parenthesis straight b 

Diketahui straight S subscript 5 equals negative 5 maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight S subscript straight n end cell equals cell straight n over 2 left parenthesis straight a plus straight U subscript straight n right parenthesis end cell row cell straight S subscript straight n end cell equals cell straight n over 2 left parenthesis straight a plus left parenthesis straight a plus left parenthesis straight n minus 1 right parenthesis straight b right parenthesis right parenthesis end cell row cell straight S subscript 5 end cell equals cell 5 over 2 left parenthesis straight a plus left parenthesis straight a plus left parenthesis 5 minus 1 right parenthesis straight b right parenthesis right parenthesis end cell row cell negative 5 end cell equals cell 5 over 2 left parenthesis 2 straight a plus 4 straight b right parenthesis end cell row cell negative 5 end cell equals cell 5 left parenthesis straight a plus 2 straight b right parenthesis end cell row cell negative 5 end cell equals cell 5 straight a plus 10 straight b end cell end table 

Diketahui straight U subscript 6 equals negative 10 maka 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript straight n end cell equals cell straight a plus left parenthesis straight n minus 1 right parenthesis straight b end cell row cell straight U subscript 6 end cell equals cell straight a plus left parenthesis 6 minus 1 right parenthesis straight b end cell row cell negative 10 end cell equals cell straight a plus 5 straight b end cell end table 

Didapatkan persamaan 5 straight a plus 10 straight b equals negative 5 dan straight a plus 5 straight b equals negative 10 

Selanjutnya cari nilai a dan b dengan cara eliminasi-substitusi kedua persamaan tersebut.

table row cell 5 straight a plus 10 straight b equals negative 5 end cell cell vertical line cross times 1 vertical line end cell cell 5 straight a plus 10 straight b equals negative 5 end cell blank row cell straight a plus 5 straight b equals negative 10 end cell cell vertical line cross times 2 vertical line end cell cell 2 straight a plus 10 straight b equals negative 20 end cell minus row blank blank cell 3 straight a equals 15 end cell blank row blank blank cell straight a equals 15 over 3 end cell blank row blank blank cell straight a equals 5 end cell blank end table  

Substitusikan nilai straight a equals 5 ke straight a plus 5 straight b equals negative 10

table attributes columnalign right center left columnspacing 0px end attributes row cell straight a plus 5 straight b end cell equals cell negative 10 end cell row cell left parenthesis 5 right parenthesis plus 5 straight b end cell equals cell negative 10 end cell row cell 5 straight b end cell equals cell negative 10 minus 5 end cell row cell 5 straight b end cell equals cell negative 15 end cell row straight b equals cell fraction numerator negative 15 over denominator 5 end fraction end cell row straight b equals cell negative 3 end cell end table 

Didapatkan nilai straight a equals 5 dan straight b equals negative 3 

Selanjutnya cari jumlah 17 suku pertama menggunakan rumus straight S subscript straight n equals straight n over 2 left parenthesis straight a plus straight U subscript straight n right parenthesis 

table attributes columnalign right center left columnspacing 0px end attributes row cell straight S subscript straight n end cell equals cell straight n over 2 left parenthesis straight a plus straight U subscript straight n right parenthesis end cell row cell straight S subscript straight n end cell equals cell straight n over 2 left parenthesis straight a plus left parenthesis straight a plus left parenthesis straight n minus 1 right parenthesis straight b right parenthesis right parenthesis end cell row cell straight S subscript 17 end cell equals cell 17 over 2 left parenthesis 5 plus left parenthesis 5 plus left parenthesis 17 minus 1 right parenthesis left parenthesis negative 3 right parenthesis right parenthesis right parenthesis end cell row cell straight S subscript 17 end cell equals cell 17 over 2 left parenthesis 10 plus 16 left parenthesis negative 3 right parenthesis right parenthesis end cell row cell straight S subscript 17 end cell equals cell 17 over 2 left parenthesis 10 minus 48 right parenthesis end cell row cell straight S subscript 17 end cell equals cell 17 over 2 left parenthesis negative 38 right parenthesis end cell row cell straight S subscript 17 end cell equals cell 17 cross times left parenthesis negative 19 right parenthesis end cell row cell straight S subscript 17 end cell equals cell negative 323 end cell end table 

Oleh karena itu, jawaban yang benar adalah D.

133

5.0 (2 rating)

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