Speed Math: Sum of Consecutive Squares

In this blog post, we will be learning the trick to sum up two consecutive squares.

Let us assume the numbers to be A, B (i.e A+1).

Rule: A² + (A+1)² = 2A² + 2A +1

Now let us look at few examples:

Example 1: 25^2 + 26^2 = 2 × 25^2 + 2 × 25 + 1 
           = 2 × 625 + 51= 1301.

Example 2: 58^2 +59^2 = 2 × 58^2 + 2 × 58 + 1  
            = 2 × [33|64] + 117 
            = 6728 +117 = 6845.

Example 3: 94^2 + 95^2 = 2 × 94^2+ 2 × 94 + 1 
           = 2 × [88|36] + 189 
           = 17672 + 189 = 17861.

Example 4: 48^2 + 49^2 =  2 × 48^2 + 2 × 48 + 1 
           = 2 × [23|04] + 97 = 4705.

Example 5:  52^2 + 53^2 = 2 ×  52^2+ 2 × 52 + 1 
             = 2 × [27|04] + 105 = 5513.

Solve the following by yourself:

• 12² + 13² =
• 97² + 98² =

Happy Learning! I hope you read the other published post where the numbers are not consecutive numbers.

“The essence of Mathematics lies in its freedom”

— Georg Cantor