The sum of first n odd natural numbers is

Options

A. `n^(2)`
B. `n(n+1)`
C. `n^(2)(n+1)^(2)`
D. `(n+1)^(2)`

Answer

A

Explanation

The series of odd number is 1,3,5,...
Hence, first term a = 1 and common difference, d = 3 -1 = 2 The sum of first n odd terms
`=n/2[2a + (n-1)d]`
`=n/2 [1+(n-1)2] = n/2 [2n] = n^(2)`