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Suatu barisan geometri diketahui  dan . Tentukan !

Pertanyaan

Suatu barisan geometri diketahui begin mathsize 14px style straight U subscript 3 equals 11 end style dan begin mathsize 14px style straight U subscript 4 equals 14 end style. Tentukan begin mathsize 14px style straight U subscript 12 end style

Pembahasan Soal:

Deret geometri dengan begin mathsize 14px style straight U subscript 3 equals 11 end style dan begin mathsize 14px style straight U subscript 4 equals 14 end style, maka 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight r equals cell straight U subscript 4 over straight U subscript 3 end cell row blank equals cell 14 over 11 end cell row blank blank blank row cell straight U subscript 3 end cell equals cell ar squared end cell row 11 equals cell straight a open parentheses 14 over 11 close parentheses squared end cell row 11 equals cell straight a 196 over 121 end cell row straight a equals cell fraction numerator 11 cross times 121 over denominator 196 end fraction end cell row straight a equals cell fraction numerator 1.331 over denominator 196 end fraction end cell end table end style  

Maka begin mathsize 14px style straight U subscript 12 end style adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript straight n end cell equals cell ar to the power of straight n minus 1 end exponent end cell row cell straight U subscript 12 end cell equals cell fraction numerator 1.331 over denominator 196 end fraction open parentheses 14 over 11 close parentheses to the power of 12 minus 1 end exponent end cell row blank equals cell 11 cubed over 14 squared open parentheses 14 over 11 close parentheses to the power of 11 end cell row blank equals cell fraction numerator 11 cubed times 14 to the power of 11 over denominator 14 squared times 11 to the power of 11 end fraction end cell row blank equals cell 14 to the power of 9 over 11 to the power of 8 end cell row blank equals cell 96 comma 4 end cell end table end style 

Jadi begin mathsize 14px style straight U subscript 12 equals 96 comma 4 end style

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 14 Maret 2021

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