Question

Wyznacz ciąg geometryczny :
a6=1, a8=9

Answer 1

a₆ = 1

a₈ = 9

 

an = a₁* q ⁿ ⁻ ¹

 

a₆ = a₁ *q⁵

a₈ = a₁ *q⁷

 

a₈/a₆ =  a₁q⁷/a₁q⁵=  q⁷ ⁻⁵ = q 2

9/1 = q²

q² = 9

q = 3

 

a₆ = a₁ *q⁵

1 = a₁ * 3⁵

1 = 243 a₁

a₁ = 1/243

 

odp. a₁ = 1/243  a   q = 3