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Diketahui , jika nilai n positif, nilai  adalah ....

Pertanyaan

Diketahui begin inline style sum from k equals 2 to 6 of end style left parenthesis n k minus 5 right parenthesis squared equals 335, jika nilai n positif, nilai 2 straight n squared minus 3 straight n adalah ....

Pembahasan Soal:

Diketahui : begin inline style sum from k equals 2 to 6 of end style left parenthesis n k minus 5 right parenthesis squared equals 335 dan nilai n positif

DItanya : nilai 2 straight n squared minus 3 straight n ?

Jawab :
Dengan menggunakan konsep notasi sigma dari deret aritmatika untuk mencari nilai n.

table attributes columnalign right center left columnspacing 0px end attributes row cell sum from straight k equals 2 to 6 of left parenthesis nk minus 5 right parenthesis squared end cell equals 335 row cell left parenthesis 2 straight n minus 5 right parenthesis squared plus left parenthesis 3 straight n minus 5 right parenthesis squared plus open parentheses 4 straight n minus 5 close parentheses squared plus open parentheses 5 straight n minus 5 close parentheses squared plus open parentheses 6 straight n minus 5 close parentheses squared end cell equals 335 row cell 4 straight n squared minus 20 straight n plus 25 plus 9 straight n squared minus 30 straight n plus 25 plus 16 straight n squared minus 40 straight n plus 25 plus 25 straight n squared minus 50 straight n plus 25 plus 36 straight n squared minus 60 straight n plus 25 end cell equals 335 row cell 90 straight n squared minus 200 straight n plus 125 end cell equals 335 row cell 90 straight n squared minus 200 straight n minus 210 end cell equals 0 row cell 9 straight n squared minus 20 straight n minus 21 end cell equals 0 end table

table attributes columnalign right center left columnspacing 0px end attributes row cell straight n subscript 12 end cell equals cell fraction numerator negative straight b plus-or-minus square root of straight b squared minus 4 straight a cross times straight c end root over denominator 2 straight a end fraction end cell row blank equals cell fraction numerator 20 plus-or-minus square root of left parenthesis negative 20 right parenthesis squared minus 4 open parentheses 9 close parentheses cross times open parentheses negative 21 close parentheses end root over denominator 2 cross times 9 end fraction end cell row blank equals cell fraction numerator 20 plus-or-minus square root of 400 plus 756 end root over denominator 18 end fraction end cell row blank equals cell fraction numerator 20 plus-or-minus square root of 1.156 end root over denominator 18 end fraction end cell row blank equals cell fraction numerator 20 plus-or-minus 34 over denominator 18 end fraction end cell end table

Karena dibilangan n-nya positif, maka n yang diambil positif yaitu :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight n subscript 1 end cell equals cell fraction numerator 20 plus 34 over denominator 18 end fraction end cell row blank equals cell 54 over 18 end cell row blank equals 3 end table

Lalu substitusi nilai n ke 2 straight n squared minus 3 straight n.

table attributes columnalign right center left columnspacing 0px end attributes row cell 2 straight n squared minus 3 straight n end cell equals cell 2 open parentheses 3 close parentheses squared minus 3 open parentheses 3 close parentheses end cell row blank equals cell 18 minus 9 end cell row blank equals 9 end table

Dengan demikian, nilai 2 straight n squared minus 3 straight n adalah 9.

Oleh karena itu, jawaban yang benar adalah E.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 18 Juni 2021

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