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Diberikan suatu barisan geometri, dengan  maka ten...

Diberikan suatu barisan geometri, dengan begin mathsize 14px style U subscript 1 plus U subscript 3 equals 3 space dan space U subscript 2 plus U subscript 4 equals 1 1 half square root of 2 equals fraction numerator 3 square root of 2 over denominator 2 end fraction end style maka tentukan :

a. Suku pertama dan rasio 

Jawaban:

table attributes columnalign right center left columnspacing 0px end attributes row cell straight U subscript 1 plus straight U subscript 3 end cell equals 3 row cell straight a plus ar squared end cell equals 3 row cell straight a open parentheses 1 plus straight r squared close parentheses end cell equals 3 row cell 1 plus straight r squared end cell equals cell 3 over straight a end cell row blank blank blank end table  

Mencari rasio (r)

table attributes columnalign right center left columnspacing 0px end attributes row cell U subscript 2 plus U subscript 4 end cell equals cell 3 over 2 square root of 2 end cell row cell a r plus a r cubed end cell equals cell 3 over 2 square root of 2 end cell row cell a r left parenthesis 1 plus r squared right parenthesis end cell equals cell 3 over 2 square root of 2 end cell row cell a r open parentheses 3 over a close parentheses end cell equals cell 3 over 2 square root of 2 end cell row r equals cell 1 half square root of 2 end cell end table 

Mencari nilai a

table attributes columnalign right center left columnspacing 0px end attributes row cell a open parentheses 1 plus r squared close parentheses end cell equals 3 row cell a open parentheses 1 plus open parentheses fraction numerator square root of 2 over denominator 2 end fraction close parentheses close parentheses end cell equals 3 row cell a open parentheses 1 plus 1 half close parentheses end cell equals 3 row cell a.3 over 2 end cell equals 3 row a equals 2 end table 

 

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