Matematika

Pertanyaan

barisan dan deret
1. 20, 26, 32,...
tentukan U5, U7, S5, S7

2. 3, 12, 48,...
tentukan U4, U8, S4, S6

2 Jawaban

  • 1.
    rumus Un = a + (n-1) .b
    rumus Sn= 1/2 n (2.a + (n-1) . b)
    u5= 20 + (5-1) . 6 =44
    u7= 20 + (7-1)  . 6 = 56
    s5= 1/2 5 ( 2.20 + (5-1) . 6) = 115
    s7= 1/2 7 (2.20 + (7-1) . 6 )= 266
    2. 
    u4= 2 + (4-1) . 1 = 5
    u8= 2 + (8-1) .1 = 9
    s4= 1/2 4 (2.2 + (4-1) . 1) = 14
    s6= 1/2 6 (2.2 + (6-1) .1) = 27
  • 1. a = 20
        b = 4
    Un = a + (n-1)b
    U₅ = 20 + 4(6))
         = 46

    U₇ = 20 + 6(6)
         = 56

    Sn = n/2 (U₁ +  Un)
    S₅ = 5/2 (20 + 46)
         = 5/2 (66)
         = 165 

    S₇ = 7/2 (20 + 56)
         = 7/2 (76)
         = 266

    2. a = 3
        r = 4

    Un = a(r)^n-1
    U₄ = 3(4)⁴⁻¹
         = 3(4)³
         = 3(64)
         = 192

    U₈ = 3(4)⁸⁻¹
         = 3(4)⁷
         = 3(16384)
         = 49152

    Sn = a(r^n - 1) / r - 1
    S₄ = 3(4⁴ - 1) / 4 - 1
         = 3(256) / 3
         = 256 

    S₆ = 3(4⁶ - 1) / 6 - 1
         = 3(4095) / 5
         = 2457


Pertanyaan Lainnya