Question

Pada deret aritmatika diketahui
U5=14 dan U7=19 tentukan:
a.U1 dan b
b.U10 dan U20
c.Jumlah 8 suku pertama

Answer 1

A. a + 6b = 19
    a + 4b = 14 _
         2b = 5
           b= 2,5
U1= 4

b. U10 = 26,5
   U20= 51,5

c. S8= 8/2 (4+4+7.2,5)
        = 4 (25,5)
       = 102

Answer 2

Un = a + (n - 1)b
U₅ = a + (5 - 1)b
14 = a + 4b    .....(1)

U₇ = a + (7 - 1)b
19 = a + 6b     ....(2)

(1) a + 4b = 14
(2) a + 6b = 19    -
         -2b = - 5
           b  = 5/2

(1) a = 14 - 4b = 14 - 4(5/2) = 14 - 10 = 4

(a). U₁ = a = 4 dan b = 5/2
(b). U₁₀ = a + 9b = 4 + 9(5/2) = 4 + (45/2)
      U₁₀ = 4 + 22 = 26

     U₂₀ = a + 19b = 4 + 19 (5/2) = 4 + (95/2)
     U₂₀ = 4 + 47 =51
(c).