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Suku ke-2 dan suku ke-5 suatu deret geometri bertu...

Suku ke-2 dan suku ke-5 suatu deret geometri berturut-turut adalah 8 dan 1. Jumlah lima suku pertama adalah ...

  1. 28

  2. 30

  3. 31

  4. 31 1 half

  5. 31 3 over 4

Jawaban:

R u m u s space s u k u space k e minus n space y a i t u colon  U subscript n equals space a r to the power of n minus 1 end exponent  r u m u s space j u m l a h space s a m p a i space s u k u space k e minus n space a d a l a h  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 comma r less than 1  D a n space u n t u k space m e n c a r i space r a s i o space a d a l a h space  r to the power of m minus n end exponent equals U subscript m over U subscript n  M a k a  r to the power of 5 minus 2 end exponent equals U subscript 5 over U subscript 2  r cubed equals 1 over 8  U subscript 2 equals a r to the power of 2 minus 1 end exponent  a equals U subscript 2 over r equals fraction numerator 8 over denominator begin display style 1 half end style end fraction equals space 16  S e h i n g g a space j u m l a h space 5 space s u k u space p e r t a m a n y a space y a i t u colon  S subscript 5 equals fraction numerator 16 left parenthesis 1 minus left parenthesis begin display style 1 half end style right parenthesis to the power of 5 right parenthesis over denominator 1 minus begin display style 1 half end style end fraction  equals fraction numerator 16 left parenthesis 1 minus left parenthesis begin display style 1 over 32 end style right parenthesis over denominator begin display style 1 half end style end fraction  equals 32 left parenthesis 1 minus 1 over 32 right parenthesis  equals 31

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