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Tentukan rasio dan suku pertama dari barisan geometri di bawah ini: a suku ke-4 dan suku ke-6

Tentukan rasio dan suku pertama dari barisan geometri di bawah ini:

a suku ke-4 begin mathsize 14px style equals 8 end style dan suku ke-6begin mathsize 14px style equals 729 end style

Jawaban:

Dengan menerapkan konsep barisan geometri:

begin mathsize 14px style straight U subscript straight n equals straight a times straight r to the power of straight n minus 1 end exponent end style 

Dengan:

begin mathsize 14px style straight U subscript 4 equals 8 straight U subscript 6 equals 729 end style 

Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 4 end cell equals cell ar cubed equals 8 end cell row cell straight U subscript 6 end cell equals cell ar to the power of 5 equals 729 end cell row cell straight U subscript 6 over straight U subscript 4 end cell equals cell ar to the power of 5 over ar cubed end cell row cell ar to the power of 5 over ar cubed end cell equals cell 729 over 8 end cell row cell straight r to the power of 5 minus 3 end exponent end cell equals cell 729 over 8 end cell row cell straight r squared end cell equals cell 729 over 8 end cell row straight r equals cell plus-or-minus square root of 729 over 8 end root end cell row blank equals cell plus-or-minus fraction numerator 27 over denominator square root of 8 end fraction end cell row blank equals cell plus-or-minus fraction numerator 27 over denominator 2 square root of 2 end fraction end cell row blank equals cell plus-or-minus fraction numerator 27 square root of 2 over denominator 4 end fraction end cell end table end style 

Untuk nilai begin mathsize 14px style straight r equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 27 square root of 2 over denominator 4 end fraction end cell end table end style Maka:

Error converting from MathML to accessible text.   

Untuk nilai Error converting from MathML to accessible text. Maka:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 4 end cell equals 8 row cell straight a times straight r cubed end cell equals 8 row cell straight a times left parenthesis negative fraction numerator 27 square root of 2 over denominator 4 end fraction right parenthesis cubed end cell equals 8 row cell straight a times left parenthesis negative fraction numerator 19.683 square root of 8 over denominator 64 end fraction right parenthesis end cell equals 8 row cell straight a times left parenthesis negative 19.683 square root of 8 right parenthesis end cell equals cell 64 times 8 end cell row cell straight a times left parenthesis negative 19.683 square root of 8 right parenthesis end cell equals 512 row straight a equals cell negative fraction numerator 512 over denominator 19.683 square root of 8 end fraction end cell row blank equals cell negative fraction numerator 512 over denominator 19.683 times 2 square root of 2 end fraction end cell row blank equals cell negative fraction numerator 256 over denominator 19.683 square root of 2 end fraction end cell row blank equals cell negative fraction numerator 256 square root of 2 over denominator 19.683 times 2 end fraction end cell row blank equals cell negative fraction numerator 128 square root of 2 over denominator 19.683 end fraction end cell end table end style 

Jadi, Rasio barisan geometri tersebut adalah begin mathsize 14px style straight r equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 27 square root of 2 over denominator 4 end fraction end cell end table end style dan begin mathsize 14px style straight a equals table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 128 square root of 2 over denominator 19.683 end fraction end cell end table end style atau Error converting from MathML to accessible text. dan Error converting from MathML to accessible text. 

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