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### Consecutive Numbers

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Date: 12/13/97 at 16:50:18
From: Justin Noah
Subject: Consecutive numbers

I don't understand what consecutive numbers are. Can you please
explain this to me ?

Thank you,
Justin Noah
```

```
Date: 12/16/97 at 11:27:55
From: Doctor Mark
Subject: Re: Consecutive numbers

Hi Justin,

Consecutive numbers are just numbers that sort of "lie next to each
other.

For instance, 2, 3, 4 are consecutive numbers, as are 131, 132, 133.
Another way of saying this is that consecutive numbers are integers
that you get by starting somewhere and then keeping on adding 1.
So five consecutive numbers starting at 24 would be 24, 24+1 = 25,
25+1 = 26, 26+1 = 27, 27+1 = 28, so the five consecutive numbers are
24, 25, 26, 27, 28.

Slightly more complicated are consecutive *even* numbers. These are
numbers that are even numbers, and "lie next to each other" in the
only way that they can: like 2, 4, 6, or 154, 156, 158, 160. That is,
to get consecutive even numbers, pick some even number, then add 2
to it, then add 2 to *that*, and so on. For instance, four consecutive
even numbers starting at 88 would be 88, 88+2 = 90, 90+2 = 92,
92 + 2 = 94, so the consecutive even numbers are 88, 90, 92, 94.
Said another way, start at some even number, then count by 2s:  88,
90, 92, 94.

Consecutive *odd* numbers are similar, except that you start at an
*odd* number, then keep adding 2. So if you want three consecutive odd
numbers starting at 17, you keep adding 2 until you have your three
numbers:  17, 17+2 = 19, 19+2 = 21; so the three consecutive odd
numbers are 17, 19, 21.

This idea sometimes gets a little confusing when you start doing
algebra, but you don't say whether that is what bothering you.  I'll

When  you want to represent consecutive numbers in algebra, you start
with the beginning number, say x, then keep adding 1 to it to get

x,

x + 1

(x+1) + 1 = x + 2

(x+2) + 1 = x + 3

and so on, so consecutive numbers can be represented as x, x+1, x+2,
and so on.

To represent consecutive even or odd numbers, you start somewhere,

x

x + 2

(x+2) + 2 = x + 4

(x+4) + 2 = x + 6

and so on.  So consecutive even *or* odd numbers are represented as x,
x+2, x+4, x+6, and so on.

Note that consecutive even *or* odd numbers are represented the *same
way* algebraically. That sounds confusing until you remember that if
you are looking for consecutive even numbers, the numbers must all be
even, so that means that you must start at an even number, so that x
must be even. If you are looking for consecutive *odd* integers, then
you have to pick x as an *odd* integer.  (This may take a while to
understand...)

Hope this helps, and write back if you have any other questions.

-Doctor Mark,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
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