Suku ke-2 dikurangi suku ke-12 suatu barisan aritmetika sama dengan 20. Suku pertama sama dengan enam kali suku ke-11. Jika suku ke-n barisan tersebut sama deng

Bab Barisan dan Deret
Matematika SMP Kelas IX

U1 = 6 x U11
a = 6 x (a + 10b)
a = 6a + 60b 
a - 6a = 60b
-5a = 60b
a =60b / -5
a = -12b

U2 - U12 = 20
a + b - a - 11b = 20
-10b = 20
b = 20/-10
b = -2

a = -12 . b
a = -12 . (-2)
a = 24

Un = 0
a + (n - 1)b = 0
24 + (n - 1) (-2) = 0
(n - 1) . (-2) = -24
n - 1 = -24 / -2
n = 12 + 1
n = 13

U2 - U12 = (a + b) - (a + 11b)
20 = -10b
b = 20 : (-10)
b = -2

U1 = 6 × U11
a = 6 × (a + 10b)
a = 6 × (a - 20)
a = 6a - 120
-5a = -120
a = 24

Un = a + (n - 1)b
0 = 24 + (n - 1)(-2)
0 = 24 - 2n + 2
2n = 26
n = 13

Semoga berguna +_+