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Jika suku pertama deret geometri adalah  dan rasio...

Jika suku pertama deret geometri adalah begin mathsize 14px style 2 end style dan rasionya adalah begin mathsize 14px style r equals m over alpha equals beta over alpha end style untuk begin mathsize 14px style m greater than 0 end style dan begin mathsize 14px style alpha end stylebegin mathsize 14px style beta end style merupakan akar-akar persamaan kuadarat begin mathsize 14px style x squared minus open parentheses 3 m plus 2 close parentheses x plus open parentheses 4 m plus 12 close parentheses equals 0 end style, maka jumlah begin mathsize 14px style 6 end style suku pertama deret tersebut adalah ....

  1. begin mathsize 14px style 10 end style 

  2. begin mathsize 14px style 63 end style 

  3. begin mathsize 14px style 243 end style 

  4. begin mathsize 14px style 728 end style 

  5. begin mathsize 14px style 4.095 end style 

Jawaban:

begin mathsize 14px style a equals 2 r equals m over alpha equals beta over alpha rightwards double arrow m equals beta x squared minus left parenthesis 3 m plus 2 right parenthesis x plus left parenthesis 4 m plus 12 right parenthesis equals 0 alpha plus beta equals 3 m plus 2 alpha plus m equals 3 m plus 2 alpha equals 2 m plus 2 alpha times beta equals 4 m plus 12 left parenthesis 2 m plus 2 right parenthesis m equals 4 m plus 12 2 m squared plus 2 m minus 4 m minus 12 equals 0 2 m squared minus 2 m minus 12 equals 0 m squared minus m minus 6 equals 0 left parenthesis m minus 3 right parenthesis left parenthesis m plus 2 right parenthesis equals 0 m equals 3 logical or m equals negative 2 m equals 3 rightwards double arrow alpha equals 8 rightwards double arrow r equals 3 over 8 rightwards double arrow a equals 2 S subscript 6 equals fraction numerator 2 left parenthesis 1 minus open parentheses begin display style 3 over 8 end style close parentheses to the power of 6 right parenthesis over denominator 1 minus begin display style 3 over 8 end style end fraction equals fraction numerator 2 left parenthesis 1 minus begin display style fraction numerator 729 over denominator 262.144 end fraction end style right parenthesis over denominator begin display style 5 over 8 end style end fraction equals fraction numerator 52.283 over denominator space 16.384 end fraction     end style  

Jadi, tidak ada jawaban yang tepat

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