Answer
$a_n=\dfrac{10}{9} 3^{n-1}$
Work Step by Step
The nth term is given by $a_n= a_1 r^{n-1}$ ...(1)
Given: $a_3=10$ and $a_6= 270$
$r^{6-3}=\dfrac{270}{10} \implies r=3$
Equation (1) gives: $a_3=a_1r^{3-1}$
Plug in $a_3=10$
$10=a_1 \times 3^2 \implies a_1=\dfrac{10}{9}$
This gives: $a_n=\dfrac{10}{9} 3^{n-1}$
Hence, $a_n=\dfrac{10}{9} 3^{n-1}$
