If you include 8 and 18 that is 11 numbers and their sum is 143 which is odd ---- Explanations (by the way, it is really not all the numbers between 8 and 18, it is just all the integers. There is an infinite number of numbers between 8 and 18, think of just 8, 8.1, 8.11, 8.111, 8.1111 etc) Here are some other fun ways to do this: One way to do it, of course is just to add 8+ 9 10 11 12 13 14 15 16 17 18 Before you add them all, consider just adding the last column, and looking at the ones column of that number. 8+9+0+1+2+....+8 that number is 53 so the sum is odd. If that numbers is even then the number is even OR Looking at just the odd numbers. The sum of even numbers is always even. An odd number and an even number is an odd number. So if the sum of the odd numbers is even then the last column will be an odd number and the total sum will be odd. The sum of odd numbers is even when there is an even number of them. Look at 2 odd numbers. (ie 3+3 =6, this is two odd numbers and their sum is even) 9,11,13,15,17 are even and there are 5 of them. This is an odd number of odd so the sum is odd. Now we know the sum of the odds and the evens is odd so the total of the last column must be odd and therefore the sum is odd. Another way is to see that the sum of the first n numbers is n(n+1)/2 We can add the sum of the first 18 numbers then subtract the sum of the first 7 numbers and what is left is the sum of the numbers 8 to 18. So in this case we have 18x19/2-8x9/2 which is (18x19-7x8)/2 this simplifies by first dividing the 18 and the 8 by 2 so we have 9x19-4x7= 171-28=143 OR What if we match up and add the 8 and the 18, the 9 and the 17, the 10 and the 16, the 11 and the 15, the 12 and the 14 and you have 13 left. This is the idea behind the formula for the first n numbers. That is 26x5+13=143
The sum of two odd numbers is even and the sum of an even number and an odd number is odd.So the sum of three consecutive odd numbers is odd but 270 is even.Ergo there are no three consecutive odd numbers that sum to 270.Three consecutive numbers that sum to 270 are 89, 90, 91.Three consecutive even numbers that sum to 270 are 88, 90, 92.
The sum of the first 100 even numbers is 10,100
8
33 = 9 + 11 + 13
The sum of the first 8 odd numbers is 64.
If you include 8 and 18 that is 11 numbers and their sum is 143 which is odd ---- Explanations (by the way, it is really not all the numbers between 8 and 18, it is just all the integers. There is an infinite number of numbers between 8 and 18, think of just 8, 8.1, 8.11, 8.111, 8.1111 etc) Here are some other fun ways to do this: One way to do it, of course is just to add 8+ 9 10 11 12 13 14 15 16 17 18 Before you add them all, consider just adding the last column, and looking at the ones column of that number. 8+9+0+1+2+....+8 that number is 53 so the sum is odd. If that numbers is even then the number is even OR Looking at just the odd numbers. The sum of even numbers is always even. An odd number and an even number is an odd number. So if the sum of the odd numbers is even then the last column will be an odd number and the total sum will be odd. The sum of odd numbers is even when there is an even number of them. Look at 2 odd numbers. (ie 3+3 =6, this is two odd numbers and their sum is even) 9,11,13,15,17 are even and there are 5 of them. This is an odd number of odd so the sum is odd. Now we know the sum of the odds and the evens is odd so the total of the last column must be odd and therefore the sum is odd. Another way is to see that the sum of the first n numbers is n(n+1)/2 We can add the sum of the first 18 numbers then subtract the sum of the first 7 numbers and what is left is the sum of the numbers 8 to 18. So in this case we have 18x19/2-8x9/2 which is (18x19-7x8)/2 this simplifies by first dividing the 18 and the 8 by 2 so we have 9x19-4x7= 171-28=143 OR What if we match up and add the 8 and the 18, the 9 and the 17, the 10 and the 16, the 11 and the 15, the 12 and the 14 and you have 13 left. This is the idea behind the formula for the first n numbers. That is 26x5+13=143
The sum of the first 1,000,000 positive even numbers is: 2 + 4 + 6 + 8 + ... + 2,000,000 The sum of the first 1,000,000 positive odd integers is: 1 + 3 + 5 + 7 + ... + 1,999,999 The difference between the two is: (2-1) + (4-3) + (6-5) + (8-7) + ... + (2,000,000-1,999,999). This is the same as: 1 + 1 + 1 + 1 + ... + 1. Well how many 1's are there? 1,000,000. So the difference is 1,000,000. Note that if the question asked for the difference between the sum of the first 1,000 positive even numbers and the sum of the first 1,000 positive odd numbers, the answer would be 1,000. The first n even numbers and odd numbers? n.
The numbers 493, 495, 497, 499, 501, 503, 505, 507 are the ones you want. There are eight of them, they are consecutive odd numbers and they sum to 4000.
The sum of the first 8 prime numbers is 77.
The sum of two odd numbers is even and the sum of an even number and an odd number is odd.So the sum of three consecutive odd numbers is odd but 270 is even.Ergo there are no three consecutive odd numbers that sum to 270.Three consecutive numbers that sum to 270 are 89, 90, 91.Three consecutive even numbers that sum to 270 are 88, 90, 92.
There can be no number with an odd sum of 8 because 8 is not odd!
17
The only thing that you can be certain about the sum is that 8 is a factor.
The sum of the first 100 even numbers is 10,100
To make 20 with three different odd numbers, we can use the numbers 1, 7, and 12. 1 + 7 + 12 = 20. These numbers are odd because they cannot be evenly divided by 2. It's important to note that there are multiple combinations of three odd numbers that can add up to 20, such as 3 + 9 + 8 or 5 + 11 + 4.
Well, honey, all you need to do is check the last digit of each number. If there's an odd number of odd digits, the sum is odd. If there's an even number of odd digits, the sum is even. So, in this case, 13 and 17 are odd, and 45 and 24 are even, which means the sum is odd without adding them all up. Easy peasy, lemon squeezy!