W ciągu geometrycznym a3=9/2, a5=2. Wyznacz wzór ogólny ciągu geometrycznego.
a₃=9/2=a₁q²
a₅=2=a₁q⁴
an=?
an=a₁q^(n-1)
a₁q²=9/2
a₁q⁴=2
(a₁q²)/(a₁q⁴)=9/4
1/q²=9/4
q²=4/9
q=2/3 v q=-2/3 q∈(-1,1)
a₁(2/3)⁴=2
a₁(16/64)=2
a₁=8
an=8*(2/3)^(n-1) v an=8*(-2/3)^(n-1)
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a₃=9/2=a₁q²
a₅=2=a₁q⁴
an=?
an=a₁q^(n-1)
a₁q²=9/2
a₁q⁴=2
(a₁q²)/(a₁q⁴)=9/4
1/q²=9/4
q²=4/9
q=2/3 v q=-2/3 q∈(-1,1)
a₁(2/3)⁴=2
a₁(16/64)=2
a₁=8
an=8*(2/3)^(n-1) v an=8*(-2/3)^(n-1)