Jika diketahui barisan geometri dengan r = 1/4 dan U8 = 1/1.024 , maka U4 - 2U5 = ... A. 1/2 B. 1/4 C. 1/6 D. 1/8

Kelas 10 Matematika
Bab Logaritma

1] U4 = U8 : r⁴
U4 = 1/1.024 : (1/4)⁴
U4 = 1/1.024 : 1/256
U4 = 1/1.024 . 256/1
U4 = 1/4

2] U5 = U4 . r
U5 = 1/4 . 1/4
U5 = 1/16

3] U4 - 2 . U5
= 1/4 - 2 . 1/16
= 4/16 - 2/16
= 2/16
= 1/8

Jawabannya D

Diketahui :
r    = 1/4
U8 = 1/1.024

Ditanya :
U4-2U5 = ??

Dijawab :
       U8 = a.r^7
1/1.024 = a*(1/4)^7
          a = (1/1.024)/((1/4)^7)
          a = (1/1.024)/(1/4^7)
          a = 1/(1.024*(1/4^7))
          a = 1/(2^10*(1/2^14))
          a = 1/(1/2^4)
          a = 1/(1/16)
          a = 16/1
          a = 16

U4 = a*r^3
     = 16*(1/4)^3
     = 16*(1/64)
     = 16/64
     = 1/4

U5 = a*r^4
      = 16*(1/4)^4
      = 16*(1/256)
      = 16/265
      = 1/16

U4-2U5 = 1/4 - (2*(1/16))
             = 1/4 - (2/16)
             = 1/4 - 1/8
             = 2/8 - 1/8
             = 1/8