Pertanyaan

Diketahui suku barisan geometri suku ke-1 = 3 2 dan suku ke-3 = 27 2 . Jumlah empat suku pertama (S 4 ) adalah ....

Diketahui suku barisan geometri suku ke-1 = $\frac{2}{3}$ dan suku ke-3 = $\frac{2}{27}$ . Jumlah empat suku pertama (S₄) adalah ....

R. Diah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Pembahasan

$a equals 2 over 3 a r squared equals 2 over 27 2 over 3 r squared equals 2 over 27 r squared equals fraction numerator begin display style 2 over 27 end style over denominator begin display style 2 over 3 end style end fraction r squared equals 1 divided by 9 r squared equals 1 divided by 3 space a t a u space r equals negative 1 divided by 3 A m b i l space r equals 1 divided by 3 S subscript n equals fraction numerator a left parenthesis 1 minus r to the power of n right parenthesis over denominator 1 minus r end fraction S subscript 4 equals fraction numerator begin display style 2 over 3 end style left parenthesis 1 minus left parenthesis begin display style 1 third end style right parenthesis to the power of 4 right parenthesis over denominator 1 minus begin display style 1 third end style end fraction S subscript 4 equals fraction numerator begin display style 2 over 3 end style left parenthesis 1 minus begin display style 1 over 81 end style right parenthesis over denominator begin display style 2 over 3 end style end fraction S subscript 4 equals 80 over 81$