Pertanyaan

S n menyatakan jumlah n suku pertama suatu deret geometri dengan rasio 2 . Nilai dari S n + 1 − S n S n + 3 − S n + 1 = ....

$S_{n}$ menyatakan jumlah $n$ suku pertama suatu deret geometri dengan rasio $2$ . Nilai dari $\frac{S _{n + 3} - S _{n + 1}}{S _{n + 1} - S _{n}} =$ ....

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah D

Pembahasan

Jadi, jawaban yang tepat adalah D

$begin mathsize 14px style fraction numerator S subscript n plus 3 end subscript space minus space S subscript n plus 1 end subscript over denominator S subscript n plus 1 end subscript space minus space S subscript n end fraction equals end style$

$begin mathsize 14px style fraction numerator fraction numerator a open parentheses r to the power of n plus 3 end exponent minus 1 close parentheses over denominator r minus 1 end fraction minus begin display style fraction numerator a open parentheses r to the power of n plus 1 end exponent minus 1 close parentheses over denominator r minus 1 end fraction end style over denominator fraction numerator a open parentheses r to the power of n plus 1 end exponent minus 1 close parentheses over denominator r minus 1 end fraction minus fraction numerator a open parentheses r to the power of n minus 1 close parentheses over denominator r minus 1 end fraction end fraction equals fraction numerator 2 to the power of n plus 3 end exponent minus 1 minus 2 to the power of n plus 1 end exponent plus 1 over denominator 2 to the power of n plus 1 end exponent minus 1 minus 2 to the power of n plus 1 end fraction equals fraction numerator 2 to the power of n plus 3 end exponent minus 2 to the power of n plus 1 end exponent over denominator 2 to the power of n plus 1 end exponent minus 2 to the power of n end fraction equals fraction numerator 2 to the power of n left parenthesis 2 cubed minus 2 to the power of 1 right parenthesis over denominator 2 to the power of n left parenthesis 2 minus 1 right parenthesis end fraction equals 6 over 1 equals 6 end style$

Jadi, jawaban yang tepat adalah D