Matematika

Pertanyaan

1. Jika suku ke-n, 5(n) =1/6n (n+2) (2n+1) maka s8 adalah....
2. Diketahui barisan bilangan. 2,4,8,14,22.....suku ke 10 ......
3. Suki barisan aritmatika suku ke 3=7 Dan Suku ke 7=15 jumlah 30 suku pertama adalah.......

1 Jawaban

  • 1) Sn = 1/6 n (n + 2)(2n + 1)
    S8 = 1/6 . 8 (8 + 2)(2.8 + 1) = 4/3 . (10) (17) = 680/3 = 226 2/3

    2) U1 = 2 = 2
    U2 = 4 = 2 + 2
    U3 = 8 = 2 + 2 + 4
    U4 = 14 = 2 + 2 + 4 + 6
    U5 = 22 = 2 + 2 + 4 + 6 + 8

    U10 = 2 + S9 = 2 + 9/2 (2a + 8b) = 2 + 9/2 (2(2) + 8(2)) = 2 + 9/2 (20) = 2 + 90 = 92

    3) U7 = a + 6b = 15
    U3 === a + 2b = 7
    -------------------------- --
    ................... 4b = 8 => b = 2
    a + 2b = 7 => a + 2(2) = 7 => a = 3
    S30 = 30/2 (2a + 29b) = 15 (2(3) + 29(2)) = 15 (6 + 58) = 15 (64) = 960

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