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Diketahui barisan geometri u n , dengan u 3 + u 4 = 9 ( u 1 + u 2 ) d an u 1 u 4 = 18 u 2 . Jumlah 4 suku pertama yang mungkin adalah...

Diketahui barisan geometri $u_{n},$ dengan $u_{3} + u_{4} = 9 (u_{1} + u_{2}) d an u_{1} u_{4} = 18 u_{2} .$ Jumlah 4 suku pertama yang mungkin adalah...

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$I n g a t space r u m u s space b a r i s a n space g e o m e t r i space colon u subscript n equals a r to the power of n minus 1 end exponent u subscript 3 plus u subscript 4 equals 9 open parentheses u subscript 1 plus u subscript 2 close parentheses a r squared plus a r cubed equals 9 open parentheses a plus a r close parentheses r squared open parentheses a plus a r close parentheses equals 9 open parentheses a plus a r close parentheses r squared equals 9 r equals plus-or-minus 3 u subscript 1 u subscript 4 equals 18 u subscript 2 a. a r cubed equals 18 open parentheses a r close parentheses fraction numerator a squared r cubed over denominator a r end fraction equals 18 a r squared equals 18 a r squared equals 18 a open parentheses 9 close parentheses equals 18 rightwards double arrow a equals 2 A m b i l space a space equals space 2 comma space r space equals space 3 s subscript 4 equals u subscript 1 plus u subscript 2 plus u subscript 3 plus u subscript 4 equals 2 plus 6 plus 18 plus 54 equals 80$