Question

Wyznacz ciąg geometryczny (an) tzn. a1 i q, wiedzac że:
a) a2=6, a3=18
b) a2=9, a3=81

Answer 1

A)
a₂ = 6
a₃ = 18
q = a₃/a₂ = 18/6 = 3
a₁q = a₂
a₁ = a₂/q = 6/3 = 2
an = a₁q(n - 1) = 2 * 3(n - 1) = 6 do potęgi (n - 1)
b)
a₂ = 9
a₃ = 81
q = a₃/a₂ = 81/9 = 9
a₁q = a₂ =9
a₁ = 9/q = 9/9 = 1
an = a₁q(n - 1) = 1 * 9(n - 1) = 9 do potęgi (n - 1)

Answer 2

A)

q = a₃ / a₂
q = 18 / 6
q = 3

a₁ = a₂ / q
a₁ = 6 / 3
a₁ = 2

b)
q = a₃ / a₂
q = 81/9
q = 9

a₁ = a₂ / q
a₁ = 9/9
a₁ = 1