0
It is quite easy to prove this using algebra.
Suppose x is the smaller of the two odd integer. The fact that x is odd means that it is of the form 2m + 1 where m is an integer.
[m integer => 2m is an even integer => 2m + 1 is odd]
The next odd integer will be x + 2, which is (2m + 1) + 2 = 2m + 3
The sum of these two consecutive odd integers is, therefore,
2m + 1 + 2m + 3 = 4m + 4 = 4(m + 1)
Since m is an integer, m+1 is an integer and so 4(m + 1) represents a factorisation of the answer which implies that 4 is a factor of the sum. In other words, the sum is a multiple of 4.
Still curious? Ask our experts.
Chat with our AI personalities
Judy
Vivi
LaoAdd your answer:
Earn +20 pts
The sum of three consecutive odd intrgers is 228 what are the inetgers?
This has no answer. The sum of three odd integers is always odd.
What are two consecutive integers for 52?
They are consecutive odd integers: 25 and 27.
The sum of two consecutive odd integers?
Are not all integers spaced out to be odd then even then odd then even etc (eg 1,2,3,4,5,6,7,8,9,10, etc) and therefore there is no such thing as two consecutive odd integers.
What is consecutive odd integers?
For any integer n, the numbers 2n + 1 and 2n + 3 are consecutive odd integers.
What is the sum of 3 consecutive odd integers that is at least 162 the minimum sum?
3 odd integers must total an odd number. 3 consecutive odd integers must total a multiple of 3. The lowest number greater than 162 which satisfies these requirements is 165, ie 53 + 55 + 57
