Question

When we combine two consecutive triangular numbers, we get a __________.

• A. Perfect square number
• B. Consecutive number
• C. Non square number
• D. None of these

Answer 1

Answer: (A)

Perfect square number

Triangular numbers are obtained by continued summation of natural numbers $1,2,3,4,5,6,7,.....$

$\therefore$ Set of triangular numbers is $1,3,6,10,15,21,\mathrm{28.....}$

When we add two triangular numbers we get a perfect square number

For example, $1+3=4=2^2$, $3+6=9=3^2$, $6+10=16=4^2$ and so on.

Hence, option $A$ is correct.