Có [tex]{a_{2}}^{2}=a_{1}\cdot a_{3}\Rightarrow \frac{a_{1}}{a_{2}}=\frac{a_{2}}{a_{3}}[/tex]
Và [tex]{a_{3}}^{2}=a_{2}\cdot a_{4}\Rightarrow \frac{a_{2}}{a_{3}}=\frac{a_{3}}{a_{4}}[/tex]
Suy ra [tex]\frac{a_{1}}{a_{2}}=\frac{a_{2}}{a_{3}}=\frac{a_{3}}{a_{4}}[/tex]
[tex]\Rightarrow \frac{a_{1}\cdot a_{2}\cdot a_{3}}{a_{2}\cdot a_{3}\cdot a_{4}}=\frac{{a_{1}}^{3}}{{a_{2}}^{3}}=\frac{{a_{2}}^{3}}{{a_{3}}^{3}}=\frac{{a_{3}}^{3}}{{a_{4}}^{3}}[/tex]
[tex]\Rightarrow \frac{a_{1}}{a_{4}}=\frac{a{_{1}}^{3}+{a_{2}}^{3}+{a_{3}}^{3}}{a{_{2}}^{3}+{a_{3}}^{3}+{a_{4}}^{3}}[/tex] (Dãy tỉ số bằng nhau)