If 2n+1 represents an odd integer, represent the next odd integer.?

Question

show work please

Answer 1

Every other integer is odd, so to get the next odd integer, you add 2 to the current integer:

(2n + 1) + 2 = 2n + 3

Answer 2

I'm going to fill in some numbers for n:

2(1)+1=3
2(2)+1=5
2(3)+1=6
2(4)+1=9
2(5)+1=11

Any number filled in for n comes out odd. For 2n+1 any number filled in would be an odd integer, so If you add one more to the equation 2n+1+1 or 2n+2, then you would get all even numbers:

2(1)+2=4
2(2)+2=6
2(3)+2=8
2(4)+2=10
2(5)+2=12

So you gotta make it 2n+3 which is 2n+1+1+1:

2(1)+3=5
2(2)+3=7
2(3)+3=9
2(4)+3=11
2(5)+3=13

And it's simple enough a child could understand it now right?

Answer 3

It's simple; since odd numbers go
1, 3, 5, 7, 9, 11, 13, ....

Notice that they differ by 2 every time. That means if
2n + 1 represents an odd integer, the next odd integer would be 2 more; i.e.

(2n + 1) + 2

Which is equal to

2n + 3

Answer 4

Replace n by n+1 to get 2(n+1) + 1 = 2n+3.

Answer 5

Odd integers are separated by 2 ==> if X is the Yth odd integer, then (X+2) is the (Y+1)th odd integer ==> if (2N+1) is the Yth odd integer, then (2N+1) + 2 = 2N+3 is the next odd integer.

2N+3

Answer 6

2n + 3 represents the next odd integer because to get to the next odd number, all you need to add is 2.

Answer 7

(2n+1)+2
so
2n+3

Answer 8

2n+1
2= n-1
2+1=n
n=3

So, it is 2n+3

Answer 9

(2n + 1) , (2n + 3)