Which term describes a number that can be represented as 2n + 1?

A number that can be expressed as (2n + 1), where (n) is any integer, represents an odd number. This expression indicates that when you take any integer (n), multiplying it by 2 produces an even result. By adding 1 to this even number, the result is always one unit higher, thus making it odd. For example, if (n = 0), then (2(0) + 1 = 1); if (n = 1), then (2(1) + 1 = 3); if (n = 2), then (2(2) + 1 = 5), and so on.

In contrast, even numbers can be represented by the form (2n) and cannot be expressed as (2n + 1) since adding 1 would always result in an odd number. Prime numbers, while they can sometimes be odd (for example, 3, 5, and 7), do not all fit the criteria since prime numbers are defined by having exactly two distinct positive divisors (1 and the number itself); the expression (2n + 1) does not