Answer :
To solve the problem of finding the sum of two consecutive odd integers where [tex]\( n \)[/tex] is the least of the two, we can follow these steps:
1. Identify the consecutive odd integers:
- The first integer is [tex]\( n \)[/tex].
- The next consecutive odd integer can be represented as [tex]\( n + 2 \)[/tex] (since the difference between any two consecutive odd integers is 2).
2. Find the sum of these two integers:
- The sum of [tex]\( n \)[/tex] and [tex]\( n + 2 \)[/tex] is calculated as:
[tex]\[ n + (n + 2) \][/tex]
3. Combine like terms:
- Simplifying the expression [tex]\( n + (n + 2) \)[/tex], we get:
[tex]\[ n + n + 2 = 2n + 2 \][/tex]
Therefore, the sum of the two consecutive odd integers, where [tex]\( n \)[/tex] is the smallest of the two, is represented by [tex]\( 2n + 2 \)[/tex].
Conclusion:
The correct answer from the given options is:
[tex]\[ \boxed{2n + 2} \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
1. Identify the consecutive odd integers:
- The first integer is [tex]\( n \)[/tex].
- The next consecutive odd integer can be represented as [tex]\( n + 2 \)[/tex] (since the difference between any two consecutive odd integers is 2).
2. Find the sum of these two integers:
- The sum of [tex]\( n \)[/tex] and [tex]\( n + 2 \)[/tex] is calculated as:
[tex]\[ n + (n + 2) \][/tex]
3. Combine like terms:
- Simplifying the expression [tex]\( n + (n + 2) \)[/tex], we get:
[tex]\[ n + n + 2 = 2n + 2 \][/tex]
Therefore, the sum of the two consecutive odd integers, where [tex]\( n \)[/tex] is the smallest of the two, is represented by [tex]\( 2n + 2 \)[/tex].
Conclusion:
The correct answer from the given options is:
[tex]\[ \boxed{2n + 2} \][/tex]
Thus, the correct choice is:
[tex]\[ \boxed{D} \][/tex]
