Note that the common ratio is
#color(white)("XXX")color(blue)(r)=(15/2)/3=(75/4)/(15/2)=(375/8)/(75/4)=color(blue)(5/2)#
Given
#color(white)("XXX")color(red)(x_1)=color(red)(3)#
and with #color(blue)(r)=color(blue)(5/2)#
#color(white)("XXX")x_2=color(red)3 * (color(blue)(5/4))^1#
#color(white)("XXX")x_3=x_2 * color(blue)r= color(red)3 * (color(blue)(5/4))^2#
#color(white)("XXX")x_4=x_3 * color(blue)r= color(red)3 * (color(blue)(5/4))^3#
from which we can imply the general formula:
#color(white)("XXX")x_color(magenta)n=color(red)3 * (color(blue)(5/4))^(color(magenta)n-1)#
