Question

How many tiles are in figure 100?
.
Figure 1
Figure 2
Figure 3

Answer 1

202

Explanation:

`in\\\\F(1)=4\:dots\\\\F(2)=F(1)+2=4+2=6\:dots\\\\F(3)=F(2)+2=F(1)+2+2=F(1)+2(2)=8\:dots\\\\As\:you\:can\:see\:in\\\\F(n)=F(1)+2(n-1)\\\\So\:with\:n=100\\\\F(100)=F(1)+2(100-1)\\\\F(100)=4+2(100)+2(-1)\\\\F(100)=4+200-2\\\\F(100)=200+2\\\\F(100)=202`