SOLUTION: Which of the following represents an odd number for any integer n? f.n+1 g.2n+1 h.3n i.3n+1

Question 126840This question is from textbook prentice hall mathematics
: Which of the following represents an odd number for any integer n?
f.n+1
g.2n+1
h.3n
i.3n+1 This question is from textbook prentice hall mathematics

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The answer to this is g ... 2n + 1.
.
Why? Because doubling any number makes it even, and then adding 1 to that even number makes
the term an odd integer.
.
Let's show an example of this. Suppose that n is an even number, say 8. Then 2n is 16 and when
you add 1 to that you get 17, an odd integer. Then suppose that n is an odd integer, say 9.
Then 2n would be 18 and adding 1 to that again makes the result an odd integer.
.
Now lets try to find examples of why the others won't necessarily give you an odd answer. Answer f
is n + 1. Suppose n was an odd integer, say 11. Then adding 1 to that value of n gives you an
answer of 12 ... and that is an even answer. Therefore, n + 1 does necessarily return an odd
answer for every value of n.
.
Answer h is 3n. Well, suppose n is 8. Then 3 times n is 24, and that is even. Therefore,
3n is not necessarily an odd value for every value of n.
.
Answer i is 3n + 1. If n is 5 then 3n is 15. When you add 1 to that you get 16, an even answer.
Therefore, 3n + 1 is not necessarily an odd value for every value of n.
.
Hope that this helps you to understand the problem a little better.

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