Pertanyaan

3 n − 1 − 3 n − 2 3 n + 1 − 3 n − 1 = ...

$\frac{3 ^{n + 1} - 3 ^{n - 1}}{3 ^{n - 1} - 3 ^{n - 2}} = ...$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah B.

Pembahasan

Ingat kembali: sehingga diperoleh perhitungan: Dengan demikian, nilai dari adalah . Jadi, jawaban yang tepat adalah B.

Ingat kembali:

a to the power of m over a to the power of n equals a to the power of m minus n end exponent comma space a not equal to 0

a over b divided by c over d equals a over b cross times d over c

sehingga diperoleh perhitungan:

$table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 to the power of n plus 1 end exponent minus 3 to the power of n minus 1 end exponent over denominator 3 to the power of n minus 1 end exponent minus 3 to the power of n minus 2 end exponent end fraction end cell equals cell fraction numerator 3 to the power of n times 3 minus 3 to the power of n times 3 to the power of negative 1 end exponent over denominator 3 to the power of n times 3 to the power of negative 1 end exponent minus 3 to the power of n times 3 to the power of negative 2 end exponent end fraction end cell row blank equals cell fraction numerator 3 to the power of n open parentheses 3 minus 3 to the power of negative 1 end exponent close parentheses over denominator 3 to the power of n open parentheses 3 to the power of negative 1 end exponent minus 3 to the power of negative 2 end exponent close parentheses end fraction end cell row blank equals cell fraction numerator up diagonal strike 3 to the power of n end strike open parentheses 3 minus begin display style 1 third end style close parentheses over denominator up diagonal strike 3 to the power of n end strike open parentheses begin display style 1 third end style minus begin display style 1 over 3 squared end style close parentheses end fraction end cell row blank equals cell fraction numerator begin display style 3 over 1 end style minus begin display style 1 third end style over denominator begin display style 1 third minus 1 over 9 end style end fraction end cell row blank equals cell fraction numerator begin display style fraction numerator 9 minus 1 over denominator 3 end fraction end style over denominator begin display style fraction numerator 3 minus 1 over denominator 9 end fraction end style end fraction end cell row blank equals cell fraction numerator begin display style 8 over 3 end style over denominator begin display style 2 over 9 end style end fraction end cell row blank equals cell 8 over 3 divided by 2 over 9 end cell row blank equals cell 8 over 3 cross times 9 over 2 end cell row blank equals cell 72 over 6 end cell row blank equals 12 end table$

Dengan demikian, nilai dari $fraction numerator 3 to the power of n plus 1 end exponent minus 3 to the power of n minus 1 end exponent over denominator 3 to the power of n minus 1 end exponent minus 3 to the power of n minus 2 end exponent end fraction$ adalah .

Jadi, jawaban yang tepat adalah B.