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.

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Solution

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,
$(n + 1)^{2} - n^{2} = n^{2} + 1 + 2 n - n^{2}$
$= 2 n + 1$ $[∵ (a + b)^{2} = a^{2} + 2 a b + b^{2}]$

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