Roboguru

Dari suatu deret aritmetika diketahui suku keenam ...

Dari suatu deret aritmetika diketahui suku keenam adalah 17  dan suku kesepuluh 33. Jumlah tiga puluh suku pertama adalah....

  1. 1.650

  2. 1.710

  3. 3.300

  4. 4.280

  5. 5.300

Jawaban:

Barisan space Aritmatika  Suku space ke minus straight n space space space space space space space space space space space space space space space space space space space space space space colon space U subscript n equals a plus left parenthesis n minus 1 right parenthesis b  Jumlah space straight n space suku space pertama space colon space S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis    Formula space diatas space akan space dipakai space dalam space penyelesaian space soal space  U subscript 6 equals 17 space rightwards arrow a plus left parenthesis 6 minus 1 right parenthesis b space equals 17 space rightwards arrow space a plus 5 b space equals 17  U subscript 10 equals 33 space rightwards arrow a plus left parenthesis 10 minus 1 right parenthesis b space equals 33 space rightwards arrow a plus 9 b equals 33 space space minus  space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space stack space space space space minus 4 b equals negative 16  space space space space space space space space space space b equals 4 with bar on top space space space

Substitusikan space straight b equals 4 space kedalam space persamaan space pertama  a plus 5 b equals 17  a plus 5 left parenthesis 4 right parenthesis equals 17  a equals 17 minus 20  a equals negative 3    Akan space dicari space straight S subscript 30 space end subscript dengan space straight a equals negative 3 comma space straight b equals 4 space dan space straight n equals 30  S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis  S subscript 30 equals 30 over 2 left parenthesis 2 left parenthesis negative 3 right parenthesis plus left parenthesis 30 minus 1 right parenthesis 4 right parenthesis  S subscript 30 equals 15 left parenthesis negative 6 plus 116 right parenthesis  S subscript 30 equals 1.650

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