Question

Which of the following is the difference between the squares of two consecutive natural number?

• A. Sum of the two numbers
• B. Difference of the two numbers
• C. Twice the sum of the two numbers
• D. Twice the difference between the two numbers

Answer 1

The correct option is A Sum of the two numbers

Let the two natural numbers be $n$ and $n-1$ where $n\ge 1$.
Difference of their squares is:
$d=n^2-(n-1{)}^2$
$d=n^2-(n^2-2n+1)$
$d=2n+1$
$d=n+(n+1)$
Hence, the difference of their squares is equal to their sum.

For example, consider the 2 numbers to be 4 and 5.
$5^2-4^2=25-16$
$5^2-4^2=9$
$5^2-4^2=5+4$