Question

Dada a pg(1,raiz de2/2,1/2,...),determine a razão é o valor de a5:a7

Answer 1

PG(1,√2/2, 1/2)
Razão q
q = √2/2 : 1 => q = √2/2

a₅ = a₁.q⁴
a₅ = 1.(√2/2)⁴
a₅ =√2⁴/2⁴
a₅ = 4/16
a₅ = 1/4

a₇ = a₁.q⁶
a₇ = 1.(√2/2)⁶
a₇ = √2⁶/2⁶
a₇ = 8/64
a₇ = 1/8

a₅ : a₇ = 1/4 : 1/8 = 1/4 . 8 = 2