By imagining a large version of your picture or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + … + 99 + 100 + 99 + …. + 3 + 2 + 1?

Question

Bright Tutorials · Accepted Answer

We know that by adding the counting numbers up and down, we get perfect squares as these sequences are to be thought of as forming a symmetric pattern around a central line. So, by adding counting numbers up and down to 100, we will get our central line with 100 dots and the rest above and below that line.
So 1 + 2 + 3 + ….. + 99 + 100 + 99 + …… + 3 + 2 + 1 = 100
2
= 10,000

Patterns in Mathematics — Question 13