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 

 111² − 109²

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`

 111² − 109² = 111² − 110² + 110² − 109²
                        = (111 + 110) + (110 + 109)
                        = 440