Diketahui dan . Jumlah delapan suku pertama deret geometri tesebut adalah...

Pertanyaan

Diketahui $U subscript 3 equals 16$ dan $U subscript 7 equals 256$ . Jumlah delapan suku pertama deret geometri tesebut adalah...

Pembahasan Soal:

Diketahui $U subscript 3 equals 16$ dan $U subscript 7 equals 256$ maka,

$table attributes columnalign right center left columnspacing 0px end attributes row cell U n end cell equals cell a r to the power of n minus 1 end exponent end cell row cell U subscript 3 end cell equals cell a cross times r to the power of 3 minus 1 end exponent end cell row 16 equals cell a cross times r squared end cell row 16 equals cell a r squared end cell row blank blank blank row cell U subscript 7 end cell equals cell a cross times r to the power of 7 minus 1 end exponent end cell row 256 equals cell a cross times r to the power of 6 end cell row 256 equals cell a r to the power of 6 end cell row blank blank blank row 16 equals cell a r squared end cell row 256 equals cell a r to the power of 6 end cell row blank blank blank row cell fraction numerator a r to the power of 6 over denominator a r squared end fraction end cell equals cell 256 over 16 end cell row cell r to the power of 6 minus 2 end exponent end cell equals 16 row cell r to the power of 4 end cell equals 16 row cell r to the power of 4 end cell equals cell 2 to the power of 4 end cell row r equals 2 row blank blank blank row 16 equals cell a r squared end cell row 16 equals cell a open parentheses 2 close parentheses squared end cell row 16 equals cell a open parentheses 4 close parentheses end cell row 16 equals cell 4 a end cell row a equals cell 16 divided by 4 end cell row a equals 4 end table$

Kemudian cari jumlah delapan suku pertama,

$table attributes columnalign right center left columnspacing 0px end attributes row cell S n end cell equals cell fraction numerator a left parenthesis r to the power of n minus 1 end exponent right parenthesis over denominator r minus 1 end fraction end cell row cell S subscript 8 end cell equals cell fraction numerator 4 left parenthesis 2 to the power of 8 minus 1 end exponent right parenthesis over denominator 2 minus 1 end fraction end cell row blank equals cell fraction numerator 4 left parenthesis 2 to the power of 7 right parenthesis over denominator 1 end fraction end cell row blank equals cell fraction numerator 4 open parentheses 128 close parentheses over denominator 1 end fraction end cell row blank equals cell 512 over 1 end cell row blank equals 512 end table$

Jumlah delapan suku pertama deret geometri tesebut adalah $512$ .

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 Juni 2021

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