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18. soal soal notasi sigma barisan- deret dan induksi matematika

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• 1. www.matematika-sma.com - 1 18. SOAL-SOAL NOTASI SIGMA, BARISAN, DERET DAN INDUKSI MATEMATIKA UN2004 1.Nilai ∑= =− 21 2 )65( n n …. A. 882 B. 1030 C. 1040 D. 1957 E. 2060 Jawab: ∑= =− 21 2 )65( n n (5.2 – 6) + (5.3 – 6) + (5.4 – 6)+…+ (5.21 – 6) = 4 + 9 + 14+ . . .+ 99 a = 4 b = 9 – 4 = 14 – 9 = 5 n = n(akhir) – (n(awal)-1) = 21 – (2-1) = 20 S n = 2 n (a + U n ) = 2 n (2a +(n-1) b) = 2 20 (2. 4 +(20-1) 5) = 10 (8 + 95) = 10 . 103 = 1030 Jawabannya adalah B EBTANAS2000 2. Diketahui ∑= =− 25 5 )2( k pk 0, maka nilai ∑= = 25 5 ... k pk A. 20 B. 28 C. 30 D. 42 E. 112 Jawab: ∑= =− 25 5 )2( k pk 0 ∑= =− 25 5 )2( k pk ∑= 25 5 2 k - ∑= = 25 5k pk 0 ∑= 25 5 2 k = ∑= 25 5k pk 2 (n(akhir) – (n(awal)-1) ) = ∑= 25 5k pk 2 (25 – (5-1) ) = ∑= 25 5k pk 2 . 21 = ∑= 25 5k pk ∑= 25 5k pk = 42 jawabannya adalah D Catatan : ∑= 25 5 2 k = 44 344 21 kalin 2...222 ++++ = 2 . 21 = 42 n = 25 – (5-1) = 21 kali EBTANAS2000 3. Suku keempat dan suku ketujuh barisan aritmetika berturut-turut adalah 17 dan 29. Suku ke 25 barisan tersebut adalah…. A. 97 B. 101 C. 105 D.109 E. 113 Jawab: U 4 = 17 = a + (n-1) b = a + 3b …(1) U7 = 29 = a + (n-1)b = a + 6b …(2) Dari (1) dan (2) a + 3b = 17 a + 6b = 29 - -3b = -12 b = 4 a + 3b = 17 a = 17 – 3b = 17 – 3.4 = 17 – 12 = 5 U 25 = a + (25 – 1)b = 5 + 24 . 4 = 5 + 96 = 101 jawabannya adalah B EBTANAS1990 4. Suatu deret aritmetika, diketahui jumlah 5 suku yang pertama = 35 dan jumlah 4 suku yang pertama = 24, suku yang ke 15 = …. A. 11 B. 25 C. 31 D. 33 E. 59