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Pertanyaan

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

  1. 1.650

  2. 1.710

  3. 3.300

  4. 4.280

  5. 5.300

A. Acfreelance

Master Teacher

Jawaban terverifikasi

Pembahasan

Barisan Aritmatika

Suku ke-n : U subscript n equals a plus left parenthesis n minus 1 right parenthesis b

Jumlah n suku pertama : S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis

Formula diatas akan dipakai dalam penyelesaian soal

U subscript 6 equals 17 rightwards arrow a plus left parenthesis 6 minus 1 right parenthesis b equals 17 space space space rightwards arrow a plus 5 b equals 17  U subscript 10 equals 33 rightwards arrow a plus left parenthesis 10 minus 1 right parenthesis b equals 33 rightwards arrow a plus 9 b equals 33 space 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 minus negative negative negative negative negative  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 space space space space minus 4 b equals negative 16  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 space space space space space space space space space b space equals 4

Substitusikan b = 4 kedalam persamaan pertama

rightwards double arrow a plus 5 b equals 17  a plus 5 left parenthesis 4 right parenthesis equals 17  a equals 17 minus 20 equals negative 3

S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis b right parenthesis rightwards arrow 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 equals 15 left parenthesis negative 6 plus 116 right parenthesis equals 1.650

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Jumlah dari deret aritmetika 17+21+25+29+33+...+577 adalah ....

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