For any integer p the odd number has the form. 

Concept -

An odd number is any integer that is not divisible by 2 without leaving a remainder. In mathematical terms, an odd number can be represented in the form (2k + 1), where ( k ) is any integer.

Explanation -
 2 x 0 + 1 = 1 (the first odd number)
 2 x 1 + 1 = 3
 2 x (-1) + 1 = -1 (negative odd number)

In general, any odd number can be obtained by taking an integer, multiplying it by 2, and then adding 1 (or subtracting 1 for negative odd numbers).

Hence the correct answer is (2p + 1).