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Tentukan 10 suku pertama barisan berikut ini! U n = 2 + 3 n n 2 − 4 n

Tentukan 10 suku pertama barisan berikut ini!

$U_{n} = \frac{n ^{2} - 4 n}{2 + 3 n}$

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Jawaban terverifikasi

Pembahasan

Suku ke-1 Suku ke-2 Suku ke-3 Suku ke-4 Suku ke-5 Suku ke-6 Suku ke-7 Suku ke-8 Suku ke-9 Suku ke-10 Jadi,10 suku pertama barisan tersebut adalah .

Suku ke-1

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 1 end cell equals cell fraction numerator 1 squared minus 4 times 1 over denominator 2 plus 3 times 1 end fraction end cell row blank equals cell fraction numerator 1 minus 4 over denominator 2 plus 3 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 5 end fraction end cell end table$

Suku ke-2

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals cell fraction numerator 2 squared minus 4 times 2 over denominator 2 plus 3 times 2 end fraction end cell row blank equals cell fraction numerator 4 minus 8 over denominator 2 plus 6 end fraction end cell row blank equals cell fraction numerator negative 4 over denominator 8 end fraction end cell end table$

Suku ke-3

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 3 end cell equals cell fraction numerator 3 squared minus 4 times 3 over denominator 2 plus 3 times 3 end fraction end cell row blank equals cell fraction numerator 9 minus 12 over denominator 2 plus 9 end fraction end cell row blank equals cell fraction numerator negative 3 over denominator 11 end fraction end cell end table$

Suku ke-4

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 4 end cell equals cell fraction numerator 4 squared minus 4 times 4 over denominator 2 plus 3 times 4 end fraction end cell row blank equals cell fraction numerator 16 minus 16 over denominator 2 plus 12 end fraction end cell row blank equals cell 0 over 14 end cell row blank equals 0 end table$

Suku ke-5

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 5 end cell equals cell fraction numerator 5 squared minus 4 times 5 over denominator 2 plus 3 times 5 end fraction end cell row blank equals cell fraction numerator 25 minus 20 over denominator 2 plus 15 end fraction end cell row blank equals cell 5 over 17 end cell end table$

Suku ke-6

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 6 end cell equals cell fraction numerator 6 squared minus 4 times 6 over denominator 2 plus 3 times 6 end fraction end cell row blank equals cell fraction numerator 36 minus 24 over denominator 2 plus 18 end fraction end cell row blank equals cell 12 over 20 end cell end table$

Suku ke-7

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 7 end cell equals cell fraction numerator 7 squared minus 4 times 7 over denominator 2 plus 3 times 7 end fraction end cell row blank equals cell fraction numerator 49 minus 28 over denominator 2 plus 21 end fraction end cell row blank equals cell 21 over 23 end cell end table$

Suku ke-8

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 8 end cell equals cell fraction numerator 8 squared minus 4 times 8 over denominator 2 plus 3 times 8 end fraction end cell row blank equals cell fraction numerator 64 minus 32 over denominator 2 plus 24 end fraction end cell row blank equals cell 32 over 26 end cell end table$

Suku ke-9

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 9 end cell equals cell fraction numerator 9 squared minus 4 times 9 over denominator 2 plus 3 times 9 end fraction end cell row blank equals cell fraction numerator 81 minus 36 over denominator 2 plus 27 end fraction end cell row blank equals cell 45 over 29 end cell end table$

Suku ke-10

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 10 end cell equals cell fraction numerator 10 squared minus 4 times 10 over denominator 2 plus 3 times 10 end fraction end cell row blank equals cell fraction numerator 100 minus 40 over denominator 2 plus 30 end fraction end cell row blank equals cell 60 over 32 end cell end table$

Jadi, 10 suku pertama barisan tersebut adalah

begin mathsize 12px style negative 3 over 5 comma space minus 4 over 8 comma space minus 3 over 11 comma space 0 comma space 5 over 17 comma space 12 over 20 comma space 21 over 23 comma space 32 over 26 comma space 45 over 29 comma space 60 over 32 end style .