Pertanyaan

Pada barisan geometri U 2 = 2 dan U 8 = 128 . Tentukan : a. Rasio (r) dan suku pertama b. Suku ke-5 c. Jumlah 8 suku pertama

Pada barisan geometri $U_{2} = 2$ dan $U_{8} = 128$ . Tentukan :

a. Rasio (r) dan suku pertama

b. Suku ke-5

c. Jumlah 8 suku pertama

F. Kartikasari

Master Teacher

Mahasiswa/Alumni Universitas Negeri Surabaya

Jawaban terverifikasi

Pembahasan

a. Rasio (r) dan suku pertama - Rasio - Suku pertama b. Suku ke-5 c. Jumlah 8 suku pertama

a. Rasio (r) dan suku pertama

- Rasio

$begin mathsize 14px style fraction numerator straight U subscript 2 equals straight U subscript 1 straight r equals 2 over denominator straight U subscript 8 equals straight U subscript 1 straight r to the power of 7 equals 128 end fraction straight r to the power of negative 6 end exponent equals 1 over 64 1 over straight r to the power of 6 equals 1 over 64 straight r to the power of 6 equals 2 to the power of 6 straight r equals 2 end style$

- Suku pertama

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 2 end cell equals cell straight U subscript 1 straight r to the power of 2 minus 1 end exponent end cell row 2 equals cell straight U subscript 1 times 2 end cell row cell straight U subscript 1 end cell equals 1 end table end style

b. Suku ke-5

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 5 end cell equals cell straight U subscript 1 times straight r to the power of 5 minus 1 end exponent end cell row blank equals cell 1 times 2 to the power of 4 end cell row blank equals 16 end table end style

c. Jumlah 8 suku pertama

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell fraction numerator U subscript 1 open parentheses r to the power of n minus 1 close parentheses over denominator r minus 1 end fraction end cell row cell S subscript 8 end cell equals cell fraction numerator 1 open parentheses 2 to the power of 8 minus 1 close parentheses over denominator 2 minus 1 end fraction end cell row blank equals 255 end table end style$