Pertanyaan

Dari suatu deret geametri diketahui suku ke-2 adalah 6 dan suku ke-6 adalah 96. Jumlah 10 suku pertama deret tersebut adalah ....

960
1.960
2.960
3.069
4.069

A. C

Master Teacher

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Pembahasan

Barisan Geometri Rumus suku ke-n:

Barisan Geometri
Rumus suku ke-n:

$U n space equals space a r to the power of n minus 1 space end exponent R u m u s space j u m l a h space n space s u k u space p e r t a m a S n space equals space fraction numerator a left parenthesis r to the power of n space minus space l right parenthesis over denominator r minus 1 end fraction space comma space u n t u k space r space greater than space 1 S n space equals space fraction numerator a left parenthesis 1 minus space r to the power of n right parenthesis over denominator 1 minus r end fraction comma space u n t u k space r space less than space 1 u 2 space equals space a r space equals space 6 space U space equals space a r to the power of 5 space equals space 96 fraction numerator U 6 over denominator U 2 end fraction equals r to the power of 5 over r equals 96 over 6 r to the power of 4 equals 16 space rightwards double arrow r equals 2 a r equals 6 space rightwards double arrow a x 2 equals 6 rightwards double arrow a equals 3 j a d i S 10 equals fraction numerator 3 left parenthesis 2 to the power of 10 minus 1 right parenthesis over denominator 2 minus 1 end fraction equals fraction numerator 3 left parenthesis 1 comma 024 minus 1 right parenthesis over denominator 1 end fraction equals 3 comma 069$