155
The sum of the first n odd numbers is n squared. 25 x 25 = 625
The sum of the even numbers is (26 + 28 + ... + 100); The sum of the odd numbers is (25 + 27 + ... + 99) Their difference is: (26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99) = 1 + 1 + ... + 1 There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38. So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.
25 of them
There is no solution. You could do it if the numbers were odd: 25 and 27 are consecutive odd numbers that equal 52.
The sum of the first 25 prime numbers is 1,060.
155
The sum of the first n positive integers (i.e. 1+2+3+...+n) is given by n(n+1)/2 so the sum of the first 25 positive integers is 1+2+3+...+25 = 25x26/2 = 325. The sum of the first 25 EVEN numbers will be double this i.e. 2+4+6+...+50 = 650.
The sum of the first 25 prime numbers is 1,060.
The sum of the first 25 numbers is 25*26/2 = 325 So the sum of the first 25 multiples of 12 is 325*12 = 3900
Oh, what a happy little question! Let's take a look at those prime numbers. When we add them up, we find that their sum is actually even. Isn't that just a delightful surprise? Remember, in the world of numbers, there's always a little bit of magic waiting to be discovered.
625
The sum of the first n odd numbers is n squared. 25 x 25 = 625
The sum of the even numbers is (26 + 28 + ... + 100); The sum of the odd numbers is (25 + 27 + ... + 99) Their difference is: (26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99) = 1 + 1 + ... + 1 There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38. So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.
By using the formula for an arithmetic series. This is basically obtained by reasoning: The sum of the first 25 numbers is the same as 25 multiplied by the average of those numbers; the average in this case is simply (1 + 25) / 2.
25 of them
Let's denote the two numbers as x and y. We know that x + y = 25 and xy = 156. By solving these two equations simultaneously, we can find the two numbers. One way to do this is by substituting y = 25 - x into the second equation, giving us x(25 - x) = 156. By solving this quadratic equation, we find that the two numbers are 12 and 13.