The set of the consecutive odd numbers 1, 3, 5, 7, ..., N has a sum of 400. How many numbers are in the set?

Question

The set of the consecutive odd numbers 1, 3, 5, 7, ..., N has a sum of 400. How many numbers are in the set?

 

Answer 1

S_n = (n/2)(a₁ + a₁ + d(n-1)), where S = sum, a₁ = first term, n = number of terms, d = common difference

 

400 = (n/2)(1 + 1 + 2(n - 1))

400 = (n/2)(2  + 2n - 2)

400 = (n/2)(2n

400 = n²

20 = n

 

Twenty numbers are in the set.