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Pertanyaan

jika dalam suatu barisan geometri u 1 ​ = 5 1 ​ dan u 1 ​ + u 2 ​ + ... + u 8 ​ = 51 maka u 251 ​ : u 250 ​ =....

jika dalam suatu barisan geometri dan maka =....

  1. 2 : 1

  2. 4 : 1

  3. 3 : 2

  4. 4 : 3

  5. 5 : 3

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A. Acfreelance

Master Teacher

Jawaban terverifikasi

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Pembahasan

Maka, Sehingga, Jadi, Jawaban A

u subscript 1 equals 1 fifth

u subscript 1 plus u subscript 2 plus horizontal ellipsis plus u subscript 8 equals 51 rightwards double arrow S subscript 8 equals 51

Maka,

S subscript 8 equals 51

fraction numerator a left parenthesis r to the power of 8 minus 1 right parenthesis over denominator r minus 1 end fraction equals 51

fraction numerator open parentheses begin display style 1 fifth end style close parentheses open parentheses r to the power of 8 minus 1 close parentheses over denominator r minus 1 end fraction equals 51

fraction numerator left parenthesis r to the power of 8 minus 1 right parenthesis over denominator r minus 1 end fraction equals 225

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left parenthesis r plus 1 right parenthesis left parenthesis r squared plus 1 right parenthesis left parenthesis r to the power of 4 plus 1 right parenthesis equals 3 cross times 5 cross times 17

Sehingga,
left parenthesis r plus 1 right parenthesis equals 3 rightwards double arrow r equals 2 space space  left parenthesis r squared plus 1 right parenthesis equals 5 rightwards double arrow r equals 2 space space  left parenthesis r to the power of 4 plus 1 right parenthesis equals 17 rightwards double arrow r equals 2

Jadi,

u subscript 251 over u subscript 250 equals fraction numerator a r to the power of 250 over denominator a r to the power of 249 end fraction equals r over 1 equals 2 over 1

Jawaban A

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