Question

Find the sum of all odd positive integers less than 450

Answer 1

Sum of all odd positive integers less than 450 is given by

1 + 3 + 5 + … + 449

a = 1

d = 2

l = 449

∴ n = `("l" - "a")/"d" + 1`

= `(449 - 1)/2 + 1`

= `448/2 + 1`

= 224 + 1 = 225

∴ S_n = `"n"/2("a" + "l")`

S₂₂₅ = `225/2(1 + 449)`

= `225/2 xx 450`

= 225²

  = 50625

Another method:

Sum of all positive odd integers = n².

We can use the formula n² = 225²

= 50625