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Jumlah suku pertama sebuah deret aritmetika ditentukan oleh rumus: Beda deret aritmetika tersebut adalah ....

Jumlah undefined suku pertama sebuah deret aritmetika ditentukan oleh rumus:

begin mathsize 14px style S subscript n equals left parenthesis 2 n minus 1 right parenthesis left parenthesis n plus 1 right parenthesis plus 1 end style 

Beda deret aritmetika tersebut adalah ....

  1. begin mathsize 14px style negative 2 end style 

  2. begin mathsize 14px style negative 1 end style 

  3. begin mathsize 14px style 0 end style 

  4. begin mathsize 14px style 1 end style 

  5. undefined 

Jawaban:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript n end cell equals cell left parenthesis 2 n minus 1 right parenthesis left parenthesis n plus 1 right parenthesis plus 1 end cell row cell S subscript 1 end cell equals cell left parenthesis 2 open parentheses 1 close parentheses minus 1 right parenthesis left parenthesis open parentheses 1 close parentheses plus 1 right parenthesis plus 1 end cell row cell S subscript 1 end cell equals cell left parenthesis 2 minus 1 right parenthesis left parenthesis 1 plus 1 right parenthesis plus 1 end cell row blank equals cell 2 plus 1 end cell row blank equals 3 end table end style

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px S subscript size 14px n end cell size 14px equals cell size 14px left parenthesis size 14px 2 size 14px n size 14px minus size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px n size 14px plus size 14px 1 size 14px right parenthesis size 14px plus size 14px 1 end cell row cell size 14px S subscript size 14px 2 end cell size 14px equals cell size 14px left parenthesis size 14px 2 begin mathsize 14px style left parenthesis 2 right parenthesis end style size 14px minus size 14px 1 size 14px right parenthesis size 14px left parenthesis begin mathsize 14px style left parenthesis 2 right parenthesis end style size 14px plus size 14px 1 size 14px right parenthesis size 14px plus size 14px 1 end cell row blank size 14px equals cell size 14px left parenthesis size 14px 4 size 14px minus size 14px 1 size 14px right parenthesis size 14px left parenthesis size 14px 2 size 14px plus size 14px 1 size 14px right parenthesis size 14px plus size 14px 1 end cell row blank size 14px equals cell size 14px 3 size 14px cross times size 14px 3 size 14px plus size 14px 1 end cell row blank size 14px equals size 14px 10 end table

Pada deret aritmatika berlaku begin mathsize 14px style S subscript n minus S subscript n minus 1 end subscript equals U subscript n end style  Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell S subscript 2 minus S subscript 1 end cell equals cell U subscript 2 end cell row cell 10 minus 3 end cell equals cell U subscript 2 end cell row 7 equals cell U subscript 2 end cell end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row Beda equals cell straight U subscript 2 minus straight U subscript 1 end cell row blank equals cell 7 minus 3 end cell row blank equals 4 end table end style

Jadi, jawaban yang tepat adalah 4

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