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Suku ke-7 dari suatu barisan geometri adalah 4.374 dan suku pertamanya = 6. Tentukan suku ke-16 pada barisan tersebut!

Pertanyaan

Suku ke-7 dari suatu barisan geometri adalah 4.374 dan suku pertamanya = 6. Tentukan suku ke-16 pada barisan tersebut!

N. Puspita

Master Teacher

Jawaban terverifikasi

Pembahasan

Diketahui :

Suku pertama barisan = a equals 6       
Suku ke-7 = U subscript 7 equals 4.374

Suku ke-7 :

table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript n end cell equals cell a r to the power of n minus 1 end exponent end cell row cell U subscript 7 end cell equals cell a r to the power of 7 minus 1 end exponent end cell row cell 4.374 end cell equals cell 6 cross times r to the power of 6 end cell row cell r to the power of 6 end cell equals cell fraction numerator 4.374 over denominator 6 end fraction end cell row cell r to the power of 6 end cell equals 729 row r equals cell plus-or-minus root index 6 of 729 end cell row r equals cell plus-or-minus 3 end cell end table

Jika r equals 3

table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript n end cell equals cell a r to the power of n minus 1 end exponent end cell row cell U subscript 16 end cell equals cell a r to the power of 16 minus 1 end exponent end cell row blank equals cell 6 cross times 3 to the power of 15 end cell row blank equals cell 6 cross times 14.348.907 end cell row blank equals cell 86.093.442 end cell end table

Jika r equals negative 3

table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript n end cell equals cell a r to the power of n minus 1 end exponent end cell row cell U subscript 16 end cell equals cell a r to the power of 16 minus 1 end exponent end cell row blank equals cell 6 cross times open parentheses negative 3 close parentheses to the power of 15 end cell row blank equals cell 6 cross times negative 14.348.907 end cell row blank equals cell negative 86.093.442 end cell end table

Maka, suku ke-16 barisan tersebut adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 86.093.442 space atau space minus 86.093.442 end cell end table

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