20. The diagram below shows a sequence of shapes made up of black and white floor tiles where each shape after the first has two more rows and two more columns than the one before it. How many black tiles would be required to create the 15 th shape in the sequence?

A 401
B 421
C 441
D 461
E 481
20. B The $n$th term of the sequence $1,3,5, \ldots$ is $2 n-1$. Therefore at the start of the solution the total number of tiles in the 15 th shape is $(2 \times 15-1)^{2}=29^{2}=841$. In each shape, there is one more black tile than white tile. Hence there would be $\frac{1}{2}(841+1)=421$ black tiles in the 15 th shape.