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Diketahui . Nilai  adalah...

Pertanyaan

Diketahui undefined. Nilai begin mathsize 14px style 7 p end style adalah... 

  1. 14

  2. 21

  3. 28

  4. 35

  5. 42

Pembahasan Video:

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 15 to 20 of p left parenthesis i minus 2 right parenthesis end cell equals 372 row cell p sum from i equals 15 to 20 of left parenthesis i minus 2 right parenthesis end cell equals 372 row cell p left parenthesis 13 plus 14 plus 15 plus 16 plus 17 plus 18 right parenthesis end cell equals 372 row cell 93 p end cell equals 372 row p equals cell 372 over 93 end cell row p equals 4 end table end style 

Nilai begin mathsize 14px style 7 p equals 7 cross times 4 equals 28 end style.

Jadi, jawaban yang tepat adalah C.

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Dijawab oleh:

F. Freelancer6

Terakhir diupdate 03 Mei 2021

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Nilai  =...

Pembahasan Soal:

begin mathsize 14px style sum from a equals 7 to 12 of open parentheses a squared plus 4 close parentheses minus sum from a equals 1 to 6 of open parentheses a squared plus 4 a minus 5 close parentheses equals sum from a equals 7 minus 6 to 12 minus 6 of open parentheses open parentheses a plus 6 close parentheses squared plus 4 close parentheses minus sum from a equals 1 to 6 of open parentheses a squared plus 4 a minus 5 close parentheses equals sum from a equals 1 to 6 of open parentheses a squared plus 12 a plus 36 plus 4 minus a squared minus 4 a plus 5 close parentheses equals sum from a equals 1 to 6 of left parenthesis 8 a plus 45 right parenthesis equals sum from a equals 1 to 6 of 8 a plus sum from a equals 1 to 6 of 45 equals 8 sum from a equals 1 to 6 of a plus sum from a equals 1 to 6 of 45 equals 8 left parenthesis 1 plus 2 plus 3 plus 4 plus 5 plus 6 right parenthesis plus 6 cross times 45 equals 8 cross times 21 plus 270 equals 168 plus 270 equals 438 end style 

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Diketahui . Nilai p yang memenuhi persamaan tersebut adalah ….

Pembahasan Soal:

Ingat kembali sifat berikut ini!

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from i equals 1 to n of i squared end cell equals cell fraction numerator n open parentheses n plus 1 close parentheses open parentheses 2 n plus 1 close parentheses over denominator 6 end fraction end cell row cell sum from i equals 1 to n of C end cell equals cell n cross times C end cell end table end style 

Dengan demikian, didapatkan penyelesaian persamaan sebagai berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from k equals 4 to 10 of open parentheses 2 open parentheses k minus 3 close parentheses squared plus 5 p close parentheses end cell equals cell sum from i equals 24 to 37 of 10 end cell row cell sum from k equals 4 minus 3 to 10 minus 3 of open parentheses 2 open parentheses open parentheses k plus 3 close parentheses minus 3 close parentheses squared plus 5 p close parentheses end cell equals cell sum from i equals 24 minus 23 to 37 minus 23 of 10 end cell row cell sum from k equals 1 to 7 of open parentheses 2 k squared plus 5 p close parentheses end cell equals cell sum from i equals 1 to 14 of 10 end cell row cell 2 sum from k equals 1 to 7 of k squared plus 5 sum from k equals 1 to 7 of p end cell equals cell sum from i equals 1 to 14 of 10 end cell row cell 2 times fraction numerator 7 open parentheses 7 plus 1 close parentheses open parentheses 2 open parentheses 7 close parentheses plus 1 close parentheses over denominator 6 end fraction plus 5 open parentheses 7 p close parentheses end cell equals cell 14 times 10 end cell row cell fraction numerator open parentheses 7 close parentheses open parentheses 8 close parentheses open parentheses 15 close parentheses over denominator 3 end fraction plus 35 p end cell equals 140 row cell 280 plus 35 p end cell equals 140 row cell 35 p end cell equals cell negative 140 end cell row p equals cell negative 4 end cell end table end style 

Jadi, jawaban yang tepat adalah D.

0

Roboguru

Nilai n yang memenuhi  adalah...

Pembahasan Soal:

begin mathsize 14px style sum from k equals 1 to n of left parenthesis 4 k plus 5 right parenthesis equals 774 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis 4 cross times 1 plus 5 right parenthesis plus left parenthesis 4 cross times 2 plus 5 right parenthesis plus left parenthesis 4 cross times 3 plus 5 right parenthesis plus... plus left parenthesis 4 cross times n plus 5 right parenthesis end cell equals 774 row cell 9 plus 13 plus 17 plus 21 plus... plus left parenthesis 4 n plus 5 right parenthesis end cell equals 774 end table end style 

Notasi sigma di atas merupakan deret aritmatika dengan begin mathsize 14px style a equals 9 comma space U subscript n equals left parenthesis 4 n plus 5 right parenthesis comma space dan space S subscript n equals 774 end style

Maka diperoleh:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell n over 2 open parentheses a plus U subscript n close parentheses end cell row 774 equals cell n over 2 left parenthesis 9 plus left parenthesis 4 n plus 5 right parenthesis right parenthesis end cell row 774 equals cell n over 2 left parenthesis 14 plus 4 n right parenthesis end cell row 774 equals cell n left parenthesis 7 plus 2 n right parenthesis end cell row 774 equals cell 7 n plus 2 n squared end cell row cell 2 n squared plus 7 n minus 774 end cell equals 0 row cell left parenthesis n minus 18 right parenthesis left parenthesis n plus 43 right parenthesis end cell equals 0 row blank blank blank end table end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis n minus 18 right parenthesis end cell equals cell 0 space space space a t a u space left parenthesis 2 n plus 43 right parenthesis equals 0 end cell row n equals cell 18 space a t a u space space space space space space space space space space space space space space n equals negative 43 over 2 subscript left parenthesis tidak space memenuhi right parenthesis end subscript end cell end table end style 

Jadi, jawaban yang tepat adalah B. 

6

Roboguru

Notasi sigma yang ekuivalen dengan  adalah...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell sum from k equals 5 to 9 of open parentheses 2 k minus 5 close parentheses squared end cell equals cell sum from k equals 5 minus 4 to 9 minus 4 of open parentheses 2 open parentheses k plus 4 close parentheses minus 5 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 2 k plus 8 minus 5 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 2 k plus 3 close parentheses squared end cell row blank equals cell sum from k equals 1 to 5 of open parentheses 4 k squared plus 12 k plus 9 close parentheses end cell row blank equals cell sum from k equals 1 to 5 of 4 k squared plus sum from k equals 1 to 5 of left parenthesis 12 k plus 9 right parenthesis end cell row blank equals cell 4 sum from k equals 1 to 5 of k squared plus sum from k equals 1 to 5 of 3 left parenthesis 4 k plus 3 right parenthesis end cell row blank equals cell 4 sum from k equals 1 to 5 of k squared plus 3 sum from k equals 1 to 5 of left parenthesis 4 k plus 3 right parenthesis end cell end table end style 

Jadi, jawaban yang tepat adalah D.

2

Roboguru

Notasi sigma yan gekuivalen dengan  adalah...

Pembahasan Soal:

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