General Form of an Even Integer

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: For some integer m, every even integer is of the form:

(a) m    (b) m + 1    (c) 2m    (d) 2m + 1

Key Concept

An even integer is any integer that is divisible by 2.

Step-by-Step Explanation

If m is any integer, then:

2m represents all integers that are divisible by 2.

Examples:

m = 0 → 2m = 0
m = 1 → 2m = 2
m = 2 → 2m = 4
m = −1 → 2m = −2

Thus, every even integer can be written in the form 2m.

Final Answer

✔ The correct form is 2m.

✔ Correct option: (c) 2m

Conclusion

Hence, for some integer m, every even integer is always of the form 2m.