How do you find sum of the first 100 odd integers?

Answer 1

Suppose t(n) is the nth term.

Then t(n) = -1 + 2n (for n = 1, 2, 3, ... 100)

Now

t(1) + t(100) = (-1 + 2*1) + (-1 +2*100) = 1 + 199 = 200

t(2) + t(99) = (-1 + 2*2) + (-1 +2*99) = 3 + 197 = 200

there are 50 such pairs.

So the grand total is 50*200 = 10000