The general form of an even number is:

• (a). 2n-1
• (b). 2n
• (c). 2n+1
• (d). 2

To determine the general form of an even number, let's analyze the options provided. An even number is defined as any integer that can be divided by 2 without leaving a remainder. This means that even numbers can be expressed in a specific mathematical form.

Identifying the Correct Option

Among the choices given:

• (a) 2n - 1
• (b) 2n
• (c) 2n + 1
• (d) 2

Let's break down each option:

Option Analysis

• 2n - 1: This expression represents an odd number. For any integer value of n, the result will always be odd. For example, if n = 1, then 2(1) - 1 = 1, which is odd.
• 2n: This is the correct representation of an even number. Here, n can be any integer (positive, negative, or zero). For instance, if n = 1, then 2(1) = 2, and if n = 2, then 2(2) = 4. Both results are even.
• 2n + 1: Similar to the first option, this expression also yields an odd number. For example, if n = 1, then 2(1) + 1 = 3, which is odd.
• 2: While this is indeed an even number, it is not a general form. It is a specific instance of an even number when n = 1.

Conclusion on the General Form

From this analysis, the general form of an even number is represented by option (b) 2n. This formula allows us to generate all even integers by substituting different integer values for n. For example:

• If n = 0, then 2(0) = 0
• If n = 3, then 2(3) = 6
• If n = -1, then 2(-1) = -2

Thus, the expression 2n effectively captures the essence of even numbers across the entire set of integers.