Question

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)

Answer 1

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