Integers from 1 to 10000 are written orderly in a grid of 100×100, as shown in the table below.
What is the sum of the numbers in the two diagonals highlighted in yellow?
Each of the diagonals is an arithmetic series.
The formula for the sum of an arithmetic series is: Sum = n(a1 + an) / 2
where n = number of terms a1 = first term an = last term
For the diagonal from upper left to lower right: n = 100 a1 = 1 an = 10000
---> Sum = 100( 1 + 10000 ) / 2 = 500 050
For the diagonal from upper right to lower left: n = 100 a1 = 100 an = 9901
---> Sum = 100( 100 + 9901 ) / 2 = 500 050
You'll need to add these two sums together to get the final answer ...