Diketahui deret aritmatika dengan U3=-1 dan U7=15, tentukanlah jumlah 8 suku pertama dan jumlah 12 suku pertama dari deret aritmatika tersebut!

jawab

u7 = 15
u3= - 1
(7-3)b = 15 -(-1)
4b = 16
b  = 4

u7 = 15
a + 6b = 15
a = 15 - 6b = 15 - 6(4) = 15 - 24  = - 9

Sn = n/2 (2a +(n-1)b)

S8 = 4 (2(-9) + 7(4))
S8 = 4 (-18 + 28)
s8 =  4(10)  = 40

S12  = 12/2 ( 2a + 11 b)
S12 = 6 (2(-9) + 11(4))
S12 = 6  ( -18 + 44) = 6(26) = 156

diketahui
U₃ = a + (3-1)b = -1 .................(1)
U₇ = a + (7-1)b = 15 ................(2)
dari (1) dan (2)
a + 2b = -1
a + 6b = 15   -
-------------------
      4b = 16
        b = 4
subtitusikan nila b = 4 ke pers. a + 2b = -1
a + 2b = -1
a + 2(4) = -1
a = -1 - 8
a = -9

S₈ = 8/2 [2a + (8-1)b]
S₈ = 4 [2(-9) + (7)(4)]
S₈ = 4 [-18 + 28]
S₈ = 4 [10]
S₈ = 40

S₁₂ = 12/2 [2a + (12-1)b]
S₁₂ = 6 [2(-9) + (11)(4)]
S₁₂ = 6 [-18 + 44]
S₁₂ = 6 [26]
S₁₂ = 156