Berikan rumus suku ke-n dari barisan 1/3, -1/9, 1/27, -1/81,..

Kelas 9
Matematika
Bab 6 - Barisan dan Deret Bilangan

barisan : 1/3, -1/9, 1/27, -1/81,..
a = 1/3

step 1 : menentukan rasio
r = u2 / u1
r = -1/9 ÷ 1/3
r = -1/3

step 2 : menentukan rumus suku ke-n
un = ar⁽ⁿ⁻¹⁾
un = 1/3 . (-1/3)⁽ⁿ⁻¹⁾

1/3, -1/9, 1/27, -1/81, ....
a = 1/3
r = (-1/9)/(1/3) = -1/9 . 3/1 = -1/3 = -1 . 1/3

Un = ar^(n - 1)
= 1/3 . (-1 . 1/3)^(n - 1)
= 1/3 . (-1)^(n - 1) . (1/3)^(n - 1)
= (-1)^(n - 1) (1/3)^(1 + n - 1)
= (-1)^(n - 1) . (1/3)^n