Properties of Consecutive Integers

We have studied about integers, integers are combination of both positive and negative numbers lying on the number line including zero. There are few important properties regarding integers that you should know:

  • Zero is also an Integer.
  • Integers which follow one another are called consecutive integers.
  • If we multiply a number by an integer and resultant value remains same then that integer is 1.

Consecutive Integers: The integers which follow one another are called consecutive integers.
For example 3, 4, 5, 6 are consecutive integers. An individual random number can never be
a consecutive integer.

Note: If we have consecutive integers in a set M from a to b i.e. M ={a,a+1,a+2,……………………..,b}.
Then number of elements in the set M is b–a+1.

Example: Set M consists of natural numbers from 75 to 199. Find the numbers of elements in set M ?

Solution: Question would have been very easy if we are asked number of natural numbers from 1 to 199. The answer to this is obviously 199. So we can also conclude it same way. From 75 to 199 we are not counting first 74 natural numbers. Hence the answer should be 199 -74= 125
Some more points about Consecutive Numbers
TOOLTIP 1
If there is odd number of digits in the set of consecutive numbers like set of three consecutive numbers (4,5,6,) or 5 digits are there, say (3,4,5,6,7), then in this case the sum of all integers is always divisible by the number of digits present in the set.
For example 2+3+4 = 9 is divisible by number of digits i.e. 3.
For example 1+2+3+4+5 = 15 is divisible by 5.

TOOLTIP 2
On the other hand ,If there are even number of digits in  set of consecutive numbers like set of four consecutive numbers (4,5,6,7) or 6 digits are there, say (3,4,5,6,7,8), then in this case the sum of all integers is never divisible by the number of digits present in the set .
For example 2+3+4+5 = 14 is not divisible by number of digits i.e. 4
For example 1+2+3+4+5+6 = 21 is not divisible by 6.




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