The total T of adding numbers from 1 to n is (n x (n+1))/2; consider if n=10:
adding 1+ 2+ 3+...+ 8+ 9+ 10= T and
adding 10+ 9+ 8+...+ 3+ 2+ 1= T (the same answer)
Now add the the two lines together--->
11+11+11+..+11+11+11= 2T, so there are 10 11s
10 x 11 =2T, divide both sides of the equal sign by 2
(10 x 11)/2 =T
So, where n=10, T=55
Consider that 1+99=100 and 2+98=100 you can continue all the way to 49+51=100. This means you have (49x100)+50 (as fifty was left at the end) this gives a final answer of 4950
Taking all the extreme numbers between 1 and 100 in each sum gives 1 + 100, 2 + 99, 3 + 98... and so on - fifty pairs of sums which add to 101. Therefore, the sum of the integers between 1 and 100 is equal to 50 x 101 = 5050.
To find the average of a set of numbers, you add all the numbers together and then divide by the total number of values. In this case, the sum of 96, 100, and 92 is 288. Dividing 288 by 3 (the total number of values) gives an average of 96.
The sum of all the first 100 even numbers is 10,100.
The sum of all the odd numbers from 1 through 100 is 10,000
The total of all of the numbers from 1 to 99 is 4950.
A scale is the total of all your numbers added up.
Add up all the numbers. Divide that total by the number of numbers you added.
All the numbers from 100 to 999 have three digits, as do all the numbers from -100 to -999, so that's 1800 in total.
- To get the arithmetic mean you add all the numbers up. Then, count the number of numbers you added, and divide the sum by the total number of numbers.
The odd numbers 1-99 will be a higher total than the even numbers 2-98
5050, ie (1 + 100) x (100/2)
Imagine all of the 100 numbers from 1 to 100 written horizontally towards the right. Then imagine another100 numbers written below the first row, but starting with 100 at the left and finishing with the number 1 on the right hand end. Now you can see what looks like 100 additions of two numbers. If you worked out those additions they would all total exactly 101, which means that altogether we have 100 pairs of numbers each totalling 101, and therefore the grand total of all 200 numbers is 101 x 100 = 10100; but 10100 is the total of two sets of numbers from 1 to 100; we want the total of one set of numbers; so we divide the 10100 by 2 which is 5050; the beauty of this method is that you don't need complicated calculations; all you need to be able to do is to multiply by 100 and to divide by 2; a very neat solution to the problem!
The average is all the numbers added together and divided by how many numbers there are. In this case: 78+100=178. 178/2=89. Therefore the mean/average of the two numbers is 89.
Usually all the integers (counting numbers) from 1 to 100.Usually all the integers (counting numbers) from 1 to 100.Usually all the integers (counting numbers) from 1 to 100.Usually all the integers (counting numbers) from 1 to 100.
You can either just add them up or use quick logic to add them in pairs: All the numbers from 1 to 49 match up with 51 through 99 to = 49 pairs of 100 = 4900, than add the two you skipped 4900 + 50 + 100 = 5050 total
The mean is the average. This can be found by dividing the total of all the numbers by the amount of numbers. For example, 15,10,13 and 16. The total is 54, and there are 4 numbers, so the mean is 54 divided by 4, 13.5. Another example, 10 and 12.5. The total is 22.5. Divided by 2 is 11.25