Question

Observe the following pattern 

2² − 1² = 2 + 1
3² − 2² = 3 + 2
4² − 3² = 4 + 3
5² − 4² = 5 + 4
and find the value of 

100² − 99²

Answer 1

From the pattern, we can say that the difference between the squares of two consecutive numbers is the sum of the numbers itself.
In a formula:

`(n+1)^2-(n)2=(n+1)+n` 

Using this formula, we get:
(i) 100² − 99²   = (99 + 1) + 99
                        = 199