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The sum of n consecutive integers is divisible by n when n is odd. It is not divisible by n when n is even. So in this case the answer is it is divisible by 25! Proof: Case I - n is odd: We can substitute 2m+1 (where m is an integer) for n. This lets us produce absolutely any odd integer. Let's look at the sum of any 2m+1 consecutive integers. a + a+d + a+2d + a+3d + ... + a+(n-1)d = n(first+last)/2 (In our problem, the common difference is 1 and this is an arithmetic series.) a + (a+1) + (a+2) + ... + (a+2m) = (2m+1)(2a+2m)/2 = (2m+1)(a+m) It is obvious that this is divisible by 2m+1, our original odd number. That proves case I when n is odd, not for case when it is even. Case II - n is even: We can substitute 2m for n. We have another arithmetic series: a + (a+1) + (a+2) + ... + (a+2m-1) = (2m)(2a+2m-1)/2 = m(2a+2m-1) It is not too hard to prove that this is not divisible by 2m... try it!
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The sum of two consecutive integers is 25?
12 and 13 :)
What are 3 consecutive integers whose sum is 75?
The integers are 24, 25 and 26.
What is two consecutive integers whose sum is 51?
25 and 26
The sum of the squares of two consecutive integers is 41 find the integers?
42 + 52 = 16 + 25 = 41
What three consecutive numbers add up to 25?
That isn't possible. The three consecutive number are assumed to be integers; the sum of three consecutive integers is always a multiple of 3 (try it out).
What are four consecutive integers whose sum is 96?
They are odd consecutive integers: 21, 23, 25 and 27.
What are three consecutive integers whose sum is 75?
They are 24, 25 and 26, as well as the consecutive odd integers 23, 25 and 27.
The sum of two consecutive integers is 25?
12 and 13 :)
What are 3 consecutive integers whose sum is 75?
The integers are 24, 25 and 26.
The sum of 3 consecutive integers is 75 what are the integers?
24 + 25 + 26 = 75
The sum of two consecutive integers is -25. which of these is one of those integers?
-13, -12
What is two consecutive integers whose sum is 51?
25 and 26
What 3 consecutive integers have a sum of 78?
25, 26 and 27
What are three consecutive integers whose sum is -78?
The three integers are -27, -26 and -25.
What are the integers of the sum of three consecutive integers are 53 more than the least of integers?
25, 26 and 27.
What are two consecutive even integers whose sum is -50?
Two consecutive even integers will be one more and one less than the quotient of their sum divided by 2. The given sum of the two consecutive integers divided by 2 is 25, so the two consecutive integers are 24 and 26.
The sum of 3 consecutive integers is 72 find the 3 integers?
The numbers are 23, 24 and 25.
