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?
+23246 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 ...
