Matematika

Pertanyaan

1. 2+5+8+11+....
Tentukanlah :
a. Bedanya
b. U10 dan U15
C. S10 Dan S15
2. -4+(-9) + (14)+(-19)
Tentukanlah :
a. Bedanya
b. U10 dan U20
c. S10 dan S20
3. Pada deret aritmatika diketahui U1 = 5 , U6=55 ,Tentukanlah :
a. Bedanya
b. U20
c. S20

Materi : Pola Bilangan, (Deret Bilangan)

1 Jawaban

  • 1. a. b = 3
    b. Un = bn + (a - b)
    Un = 3n + (2 - 3)
    Un = 3n - 1
    U10 = 3.10 - 1
    = 30 - 1
    U10 = 29
    U15 = 3.15 -1
    = 45 - 1
    U15 = 44
    c. Sn = 1/2n [2a + (n - 1) b]
    S10 = 1/2.10 [2.2 + (10 - 1) 3]
    = 5 (4 + 9 . 3)
    = 5 (4 + 27)
    = 5.31
    S10 = 155
    S15 = 1/2.15 [2.2 + (15 - 1) 3]
    = 1/2.15 (4 + 14 . 3)
    = 1/2.15 (4 + 42)
    = 1/2.15.44
    = 15.22
    S15 = 330
    2. a. b = -5
    b. U10 = -5.10 + 1
    = -50 + 1
    U10 = -49
    U20 = -5.20 + 1
    = -100 + 1
    U20 = -99
    c. S10 = 1/2.10 [2.-4 + (10 - 1) -5]
    = 5 (-8 + 9 . -5)
    = 5 (-8 + -45)
    = 5.-53
    S10 = -265
    S20 = 1/2.20 [2.-4 + (20 - 1) -5]
    = 10 (-8 + 19 . -5)
    = 10 (-8 + -95)
    = 10.-103
    S20 = -1030
    3. a. b = 55-5/6-1
    = 50/5
    b = 10
    b. U20 = 10.20 - 5
    = 200 - 5
    U20 = 195
    c. S20 = 1/2.20 [2.5 + (20-1) 10]
    = 10 (10 + 19 . 10)
    = 10 (10 + 190)
    = 10.200
    S20 = 2000

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