Carilah rasio dari barisan 3, √3, 1……dan tentukan besarnya suku ke 11

Carilah rasio dari barisan 3, √3, 1……dan tentukan besarnya suku ke 11

Jawaban : rasionya adalah 3^(-1/2) dan suku ke-11 adalah 1/81

Ingat!
Rumus mencari rasio
r = Un : (Un-1)

Mencari suku ke -n (Un)
Un = arⁿ⁻¹

dengan
r = rasio
Un = suku ke-n
a = suku ke – 1 (U1)

Pembahasan
U1 = a =3
U2 = √3

mencari rasio
r = U2 : U1
= √3 : 3
= 3^(1/2) : 3^(1)
= 3^(1/2 – 1)
= 3^(1/2 – 2/2)
= 3^[(1 – 2)/2] = 3^(-1/2)

besar suku ke-11 maka n = 11
Un = arⁿ⁻¹
U11 = 3 × [3^(-1/2)]^(11 – 1)
= 3 × [3^(-1/2)]^(10)
= 3 × 3^(-1/2 × 10)
= 3 × 3^(-10/2)
= 3 × 3^(-5)
= 3^(1 + (-5))
= 3^(1-5)
= 3^(-4)
= 1/3^(4)
= 1/81

Jadi, rasionya adalah 3^(-1/2) dan suku ke-11 adalah 1/81

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