Question

Write the 5th and 6th terms of triangular numbers. What square number do we get if we add these two numbers?Plz give the answer with details and step by step.

Answer 1

1, 3, 6 , 10, 15 , 21 , 28 , 45,.....

Above sequence shows the a pattern

of dots which form a triangle.

* 1 dot

*
* * 3 dots

*
* *
* * * 6 dots

Formula for n th triangular number:

Tn = [ n (n+1)/2]

1) if n= 5,

The 5th triangular number

=[5 (5+1)]/2

= (5 × 6)/2 = 5×3 =15

2) if n= 6,

The 6th triangular number

= [ 6 ( 6 + 1 )/2 ]

= ( 6 × 7 )/ 2

= 3× 7

= 21

Sum of the 5 th and 6th

Triangular numbers = 15 + 21

= 36

= 6 ^2

Therefore,

Required squared number = 6 ^2