How can an even number be expressed in algebraic terms?

An even number can be expressed in algebraic terms as 2n, where n is any integer. This representation is based on the definition of even numbers, which are multiples of 2. When you multiply any integer (n) by 2, the result is guaranteed to be even.

For instance, if n is 1, then 2n equals 2. If n is 2, then 2n equals 4. Continuing this pattern, you can see that as n takes on values like 0, 1, 2, 3 (and so forth), the results will always be even (0, 2, 4, 6, ...).

In contrast, the other options do not yield even numbers in all cases. For example, 2n - 1 will produce odd numbers (for any integer n). Similarly, 2n + 1 also results in odd numbers. The option n² can yield either even or odd numbers depending on the integer value of n.

Hence, the expression 2n stands out as the standard algebraic representation for even numbers, as it consistently represents multiples of 2.