If you know how to solve word problems involving the sum of consecutive even integers, you should be able to easily solve word problems that involve the sum of consecutive odd integers. The key is to have a good grasp of what odd integers are and how consecutive odd integers can be represented.
Odd Integers
If you recall, an even integer is always 22 times a number. Thus, the general form of an even number is n=2kn=2k, where kk is an integer.
So what does it mean when we say that an integer is odd? Well, it means that it’s one less or one more than an even number. In other words, odd integers are one unit less or one unit more of an even number.
Therefore, the general form of an odd integer can be expressed as nn is n=2k-1n=2k−1 or n=2k+1n=2k+1, where kk is an integer.
Observe that if you’re given an even integer, that even integer is always in between two odd integers. For instance, the even integer 44 is between 33 and 55.
