Sum of odd numbers from 1 to 100?

Question

Sum of odd numbers from 1 to 100?

Answer 1

I learned this trick to make it much faster from my high school math teacher and it helps a lot.

1+99=100

3+97=100

5+95=100

As you can see it will add up to 100 each time you do this. Seeing as we are only adding up the odd numbers we have 25 pairs.

So instead of adding all the numbers up we can just multiply 100*25=2500

the answer is 2500.

a good way to put this trick into a more usefull way would be to tell you to do this

(First term + last term)  * number of pairs

so suppose you want to add up all the numbers between one and 100

you would take

(1+100) 50

5050 would be your answer to that problem

For any sequence that does a pattern like that you can use this trick.

But remember the answer to this problem is 2500.

Answer 2

The sum of all numbers 1-100 is 5050.

1 + 100 = 101

2 + 99 = 101

3 + 98 = 101

repeat 50 times and get 5050

So if half of them are odd, then the answer has to be 2525

Answer 3

1 to 49  is    n ( n+1 )/2   n=49

now make k= 2n+1  and go 1 to 99

the easy way tho is to observe sums of odd numbers equals a perfect square

1  4  9 .....    50 squared

Answer 4

1 + 3 + 5 + 7 + 9 + ... + 97 + 99

Look at the first and last numbers:

1 + 99

Then the next two:

3 + 97

Then the next two

5 + 95

etc.

49 + 51

They all add up to 100 and you have 25 pairs.

Answer:

2500

Another way is to notice that:

1 = 1²

1 + 3 = 2²

1 + 3 + 5 = 3²

so

1 + 3 + ... + 97 + 99 = [ 100/2 ] ² = 50² = 2,500

Answer 5

The odd numbers from 1 to 99 are

Here a=1

        d= 2

l=last term = 99

find n the numbers of terms

use the formula

  l=a + (n-1) d

  99 = 1 +(n-1)2

   n-1=49

   n =50

Using the formula for the sum of n terms

    S=(n/2){a+l}

      =(50/2){1+99}

       =25*100

       =2500

Using the the formula the sum of A.P.

  

Answer 6

add odd numbers together 1, 3, 5, 7, 9, 11, ......99