Question

Question 75

In the following question, state whether the statement is True (T) or False (F):

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

Answer 1

True
Let n and n + 1 be any two consecutive numbers, then their sum = n + n + 1 = 2n + 1
Now, the difference of their squares,
$(n+1{)}^2-n^2=n^2+1+2n-n^2$
$=2n+1$ $[\because (a+b{)}^2=a^2+2ab+b^2]$