How can we express the nth odd integer mathematically?

The nth odd integer can be expressed mathematically as 2n - 1. This expression is derived from the observation that odd integers form the sequence 1, 3, 5, 7, 9, ... Each term in this sequence can be generated by substituting n with sequential positive integers.

When n equals 1, plugging it into the formula gives 2(1) - 1 = 1, which is the first odd integer. For n equals 2, the calculation results in 2(2) - 1 = 3, yielding the second odd integer. Continuing this pattern, when n is 3, the formula provides 2(3) - 1 = 5, the third odd integer. The pattern continues consistently, affirming that this formula accurately represents the sequence of odd integers.

This logical progression illustrates why the expression 2n - 1 is the correct mathematical representation for the nth odd integer.