[tex]b_1 + b_3 = 40\\b_1 + b_1\cdot q^2 = 40\\b_1(1 + q^2) = 40[/tex]
[tex]b_2 + b_4 = 80\\b_1\cdot q + b_1 \cdot q^3 = 80\\b_1(q + q^3) = 80[/tex]
Daca facem raportul acum:
[tex]\frac{b_1(1 + q^2)}{b_1(q+q^3)} = \frac{40}{80}\\\frac{1+q^2}{q(1+q^2)} = \frac{1}{2}\\\frac{1}{q} = \frac{1}{2}\Rightarrow q = 2[/tex]
[tex] b_1(1 + q^2) = 40\Rightarrow b_1 = \frac{40}{1 + q^2} = \frac{40}{1 +2^2} = \frac{40}{1 + 4} = \frac{40}{5} = 8[/tex]
