Question

When we take the difference between squares of consecutive triangular numbers, we get _______.

• A. perfect squares
• B. perfect cubes
• C. triangular numbers
• D. natural numbers

Answer 1

The correct option is B perfect cubes

The triangular numbers are 1, 3, 6, 10, 15, 21, 28, 36, 45, so on....

We will see the pattern:
$3^2$ - $1^2=8=2^3$
$6^2$ - $3^2=27=3^3$
${10}^2$ - $6^2=64=4^3$
${15}^2$ - ${10}^2=125=5^3$ and so on....

So from the pattern, it is clear that difference of perfect squares of consecutive triangular numbers is a perfect cube.