Consecutive Integers

An integer is a whole number, positive, negative or even 0. There are a number of studies with integers and consecutive-integers are one of those.

Consecutive Integer

An integer which is followed next in order is called the consecutive integer of the given integer. In other words, the difference between these integers is 1. Statistically, in a set of such consecutives, the median of the data is same as mean of the data.

3 Consecutive Integers

Let us understand the concept of consecutive with a few examples. 1, 2, 3 is a set of such since the difference between the integers is constant and the items in the set follow an order. On the other hand 1, 5, 7 is not a set of consecutive as because there is no order is maintained.

Find three Consecutive Integers                                                

We had shown an example of three consecutives as 1, 2, 3. Similarly 3, 2, 1 can also be an example even though the order in the latter case is descending.  For a perfect set of continuous-integers, the difference between these must be 1. To generalize, we can say a set of three consecutive-integers is n, (n + 1), (n + 2), where ‘n’ is any integer. This can be used as a formula to find the three.

Sum of Consecutive Integers                                                

Suppose we take a set of consecutive numbers 5, 6, 7. We can say the sum of these integers is 5 + 6 + 7 = 18. 18 also can be obtained as (3/2)(5 + 7), that is, (half the number of terms)*(first term + the last term). This can be verified with any type of integers and hence this is the formula to find the sum of consecutive-integers.

Problems:

With  these integers, mainly we come across problems like finding the numbers when the sum is given. We use the definition of continuous-integers and solve algebraically. For example if the sum of three consecutive is 24, the numbers can be found as, (n) + (n + 1) + (n + 2) = 24. We get n = 7 and hence the integers are 7, 8 and 9.

Word Problems:

The concept of consecutive-integers is very helpful in real life situations. It can be described through word problems. Suppose you buy fruits for $10 on the first day and your purchase increases by $1 each day. What is the total sum you spent for 5 days?
The fifth day expense is $14 and using the formula the total sum spent is (5/2)($10 + $14) = $60.