Consecutive NumbersDate: 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 answer it anyway. 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, then add 2, then add 2 more, and so on: 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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