Final answer:
The nth term formula for the number of square tiles in the nth figure is n².
Step-by-step explanation:
The formula for the number of square tiles in the nth figure is n². To understand this, imagine taking (n-1) from the last term and adding it to the first term. This gives us 2[1+(n-1)+3+...+(2n-3)+(2n-1)-(n-1)] = 2[n+3+...+(2n-3)+n]. Now, take (n-3) from the penultimate term and add it to the second term, which gives us 2[n+n+...+n+n] = 2n².