Pertanyaan

Hitunglah U n dan S n pada deret geometri berikut 14 , − 7 2 , 7 , ... ( n = 6 )

Hitunglah $U_{n}$ dan $S_{n}$ pada deret geometri berikut

$14$ , $- 72$ , $7$ , ... $(n = 6)$

N. Mustikowati

Master Teacher

Mahasiswa/Alumni Universitas Negeri Jakarta

Jawaban terverifikasi

Pembahasan

Diketahui: , , , ... Ditanya: Jawab:

Diketahui: , , , ...

Ditanya:

Jawab:

$begin mathsize 14px style a equals 14 r equals fraction numerator negative 7 square root of 2 over denominator 14 end fraction equals negative 1 half square root of 2 U subscript 6 equals a r to the power of 5 equals 14 open parentheses negative 1 half square root of 2 close parentheses to the power of 5 U subscript 6 equals negative 14 over 8 square root of 2 equals negative 7 over 4 square root of 2 end style$

$begin mathsize 14px style S subscript 6 equals fraction numerator a left parenthesis 1 minus r to the power of n right parenthesis over denominator 1 minus r end fraction equals fraction numerator 14 open parentheses 1 minus open parentheses negative begin display style 1 half end style square root of 2 close parentheses to the power of 6 close parentheses over denominator 1 minus open parentheses negative begin display style 1 half end style square root of 2 close parentheses end fraction S subscript 6 equals fraction numerator 14 open parentheses 1 minus begin display style 1 over 8 end style close parentheses over denominator 1 plus begin display style 1 half end style square root of 2 end fraction equals fraction numerator begin display style 49 over 4 end style over denominator begin display style fraction numerator 2 plus square root of 2 over denominator 2 end fraction end style end fraction S subscript 6 equals 49 over 4 times fraction numerator 2 over denominator 2 plus square root of 2 end fraction equals fraction numerator 49 over denominator 2 left parenthesis 2 plus square root of 2 right parenthesis end fraction times fraction numerator 2 minus square root of 2 over denominator 2 minus square root of 2 end fraction S subscript 6 equals fraction numerator 49 open parentheses 2 minus square root of 2 close parentheses over denominator 4 end fraction end style$