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Which set of numbers gives the correct possible values of \( \ell \) for \( n = 3 \)?

A. \( 0, 1, 2 \)

B. \( 0, 1, 2, 3 \)

C. \( -2, -1, 0, 1, 2 \)

D. [tex]\( -3, -2, -1, 0, 1, 2, 3 \)[/tex]

Sagot :

GinnyAnswer
To determine the correct set of possible values for \( n = 3 \), we need to consider all the integers in a specific range. Here’s a step-by-step explanation:

1. Identify the Range:
We are given \( n = 3 \). The range of integers we need to consider includes all integers starting from \(-n\) to \( n \).

2. Generate the Set:
- The minimum value in the set will be \(-n\). For \( n = 3 \), this is \(-3\).
- The maximum value in the set will be \( n \). For \( n = 3\), this is \(3\).

3. List All Integers:
We list all integers starting from \(-n\) to \( n \), inclusive. This means we include \(-3, -2, -1, 0, 1, 2, 3\).

4. Verify the Correct Set:
Now that we have listed the integers, we can verify the correct set:
- The numbers \(-3, -2, -1, 0, 1, 2, 3\) cover all integers from \(-3\) to \(3\).

Therefore, the correct possible values for \( n = 3 \) are:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]

Thus, the correct choice among the given options is:
[tex]\[ -3, -2, -1, 0, 1, 2, 3 \][/tex]
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