By the ratio test, the series diverges since the limit

is not finite.
The series only converges for x = 1/4.
(20*16 ft^2)(144 in^2/ft^2)(tiles/(10*10 in^2)
320ft^2(144in^2/ft^2)(tiles/100in^2)=460.8 tiles
However tiles are quantized integer units so 461 tiles will be needed to tile the kitchen.
C.quadratic. Based on the pattern it is quadratic.