geometric sequence:
find 1st term a5= 405 a8= 10935
\(\begin{array}{|lcrl|} \hline a_1 = a &=& \ ?\\ a_5 = 405 &=& a\cdot r^4 \\ a_8 = 10935 &=& a\cdot r^7 \\ \hline \end{array} \)
\(\begin{array}{|rcll|} \hline \frac{a_8}{a_5} = \frac{10935}{405} &=& \frac{a\cdot r^7 }{a\cdot r^4 } \\ \frac{10935}{405} &=& \frac{ r^7 }{ r^4 } \\ \frac{10935}{405} &=& r^3 \\ 27 &=& r^3 \\ \mathbf{3} & \mathbf{=} & \mathbf{r} \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline a_5 = 405 &=& a\cdot r^4 \\ 405 &=& a\cdot 3^4 \\ 405 &=& a\cdot 81 \\ a &=& \frac{405}{81} \\ \mathbf{a} & \mathbf{=} & \mathbf{5} \\ \hline \end{array}\)
The 1st term is 5.