Math CentralQuandaries & Queries


Question from Erin, a parent:

I'm having trouble with consecutive integers. i know it goes n + n + 1 + n + 2
and so on, but if its odd then do the numbers chang to odd ones? i don't know

the question is: the sum of four consecutive odd integers is -72. write an equation to model
this situation and find the values of the four integers

Think in terms of "consecutive odd integers" rather than "odd consecutive integers".

Here's your hint: Consecutive _even_ integers could be expressed as 2n, 2n+2, 2n+4,...,2n+2a.

Good Hunting!


Hi Erin,

The odd integers are ... -7, -5, -3, -1, 1, 3, 5, 7, ... so for example 5 and 7 are consecutive odd integers and so are -3 and -1. You are asked to write an equation so you need an algebraic way to express the odd integers. Even integers are easier. Every even integer is twice some other integer so algebraically I can write any even integer as 2n where n is some integer. An odd integer is one more than an even integer so you can write an odd integer as 2n + 1 where n is some integer. One more than this is an even integer so the next odd integer is 2n + 3. After that comes 2n + 5 and so on.

I hope this helps,

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