0
64
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
The sum of all numbers from 8 to 18 is an even number?
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
What 3 consecutive odd numbers total 270?
Since 270 is an even number, then three consecutive odd numbers cannot add to 270. ,because Odd + odd = even (2 numbers_ Even + odd = odd ( plus a third number) odd + odd = even (plus a fourth number) even + odd = odd (plus a fifth number) Notice from the table that the third odd number gives an odd answer; not an even answer. e.g. three odd numbers 3,5, & 7. 3 + 5 = 8 (even) 8 + 7 = 15 ( odd) et. seq.,
What is the sum of the first 100 even numbers the sum of the first 5 even numbers is 2 4 6 8 1030?
The sum of the first 100 even numbers is 10,100
What is the greatest whole number that MUST be a factor of the sum of any four consecutive positive odd numbers?
8
What is the sum of all odd numbers between 8 and 14?
33 = 9 + 11 + 13
What is the sum of the first 8 odd number?
The sum of the first 8 odd numbers is 64.
The sum of all numbers from 8 to 18 is an even number?
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
Find the difference between the sum of the first 1000000 positive even numbers and the sum of the first 1000000 positive odd numbers?
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.
If the sum of 8 consecutive odd numbers is 4000 what are the numbers?
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.
What is the sum ofthe first 8 prime numbers?
The sum of the first 8 prime numbers is 77.
What 3 consecutive odd numbers total 270?
Since 270 is an even number, then three consecutive odd numbers cannot add to 270. ,because Odd + odd = even (2 numbers_ Even + odd = odd ( plus a third number) odd + odd = even (plus a fourth number) even + odd = odd (plus a fifth number) Notice from the table that the third odd number gives an odd answer; not an even answer. e.g. three odd numbers 3,5, & 7. 3 + 5 = 8 (even) 8 + 7 = 15 ( odd) et. seq.,
What odd number is between 21 and 40 with a odd sum of 8?
There can be no number with an odd sum of 8 because 8 is not odd!
What is an odd prime numbers less than 75 if the sum of the digit is 8?
17
How can you determine whether the sum of several numbers such as 13 45 24 17 is even or odd without actually calculating the sum?
Just add the end numbers, so 3 + 5 + 4 + 7 = 19 which is odd. Alternatively, ignore even numbers [such as 4], and two odd numbers [3 and 5] added always make an even number [8], which leaves and odd number [7] so the answer will be odd. Example; five hundred different numbers, where 483 are even and 17 are odd, then no matter what the actual 500 numbers are the answer will be odd, as there is an odd [17] quantity of odd numbers.
What can you say about the factors of the sum of any four consecutive positive odd numbers?
The only thing that you can be certain about the sum is that 8 is a factor.
What is the sum of the first 100 even numbers the sum of the first 5 even numbers is 2 4 6 8 1030?
The sum of the first 100 even numbers is 10,100
What is the greatest whole number that MUST be a factor of the sum of any four consecutive positive odd numbers?
8
