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Tentukan formula suku ke- dari setiap barisan bilangan berikut ini.

Tentukan formula suku ke-begin mathsize 14px style n end style dari setiap barisan bilangan berikut ini.
begin mathsize 14px style 2 comma space 5 comma space 10 comma space 17 comma space 26 comma space horizontal ellipsis end style 

Jawaban:

Pada barisan begin mathsize 14px style 2 comma space 5 comma space 10 comma space 17 comma space 26 comma space horizontal ellipsis end style  

begin mathsize 14px style 2 comma space space space space space 5 comma space space space 10 comma space space space space space 17 comma space space space space 26 comma space horizontal ellipsis rightwards double arrow a equals 1 space space plus 3 comma space space plus 5 comma space space plus 7 comma space space plus 9 space space space space space space space space space rightwards double arrow b equals 3 space space space space space space space space plus 2 comma space space plus 2 comma space space plus 2 space space space space space space space space space space space space rightwards double arrow c equals 2  table attributes columnalign right center left columnspacing 2px end attributes row cell U subscript n end cell equals cell a plus open parentheses n minus 1 close parentheses b plus fraction numerator open parentheses n minus 2 close parentheses open parentheses n minus 1 close parentheses c over denominator 2 end fraction end cell row blank equals cell 1 plus open parentheses n minus 1 close parentheses 3 plus fraction numerator open parentheses n minus 2 close parentheses left parenthesis n minus 1 right parenthesis 3 over denominator 2 end fraction end cell row blank equals cell 1 plus 3 n minus 3 plus fraction numerator open parentheses n squared minus 3 n plus 2 close parentheses open parentheses 3 close parentheses over denominator 2 end fraction end cell row blank equals cell 3 n minus 2 plus fraction numerator 3 n squared minus 9 n plus 6 over denominator 2 end fraction end cell row blank equals cell 6 n minus 4 plus 3 n squared minus 9 n plus 6 end cell row cell U subscript n end cell equals cell 3 n squared minus 3 n plus 2 end cell end table end style 

 

Jadi,  formula suku ke-begin mathsize 14px style n end style dari setiap barisan bilangan begin mathsize 14px style 2 comma space 5 comma space 10 comma space 17 comma space 26 comma space horizontal ellipsis end style  adalah begin mathsize 14px style U subscript n equals 3 n squared minus 3 n plus 2 end style 

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