[tex]b_{3}-b_{1}=16 \Rightarrow b_{1}*q^{2}-b_{1} =16 \Rightarrow b_{1}(q^{2}-1)=16\\b_{4}-b_{2}=48 \Rightarrow b_{1}*q^{3}-b_{1}*q=48 \Rightarrow b_{1}(q^{3}-q)=48\\\\\frac{b_{1}(q^{2}-1)}{b_{1}(q^{3}-q)}=\frac{16}{48} \Rightarrow \frac{(q^{2}-1)}{(q^{3}-q)}=\frac{1}{3} \Rightarrow \frac{(q^{2}-1)}{q(q^{2}-1)}=\frac{1}{3} \Rightarrow \frac{1}{q}=\frac{1}{3} \Rightarrow q=3[/tex]
Ratia a fost notata cu litera q.
