State whether the statements are true (T) or false (F).

The difference of the squares of two consecutive numbers is their sum.

Let two consecutive numbers be x and (x + 1).

Then square of these numbers are x² and (x + 1)².

Difference of squares of these consecutive numbers = (x + 1)² – x²

= x² + 1 + 2x – x² [∵, (a + b)² = a² + b² + 2ab)

= 2x + 1

= x + x + 1

= (x) + (x + 1)

= sum of the two consecutive numbers x and x+1

Thus, difference of squares of two consecutive numbers = sum of the same consecutive numbers.

Hence, the statement is true.