What is the sum of the first 100 odd numbers using a pattern?

Answer 1

1 = 1 = 1^21+3 = 4 = 2^2

1+3+5 = 9 = 3^2

1+3+5+7 = 16 = 4^2

Thus the pattern is that the sum if the first n odd numbers is n^2 or

1+3+...+(2n-1) = n^2

So, putting n = 100, gives the sum as 100^2 = 10000.