by Yesterday , while practicing my mathamentics problems , I discovered a new technique . Maybe this technique is already discovered but yet I was happy to understand myself rather searching on Google.
So , here is the technique to find sum of consecutive numbers –
First , You need to find total set of numbers. This could be found with this formula
Largest number – smallest number +1
Ex1- 1,2,3,4,5,6,7,8,9 .
Smallest number-1
Largest number-9
, Here, total set of numbers are 9-1+1 = 9 .
Ex2- 5,6,7,8,9,10,11,12
Smallest number-5
Largest number- 12
, here total set of numbers are 12-5+1 = 8 . You can count the numbers as well to find total set of numbers .
Now , here two cases arise
1st CASE – when the total set of numbers is odd.
Ex1 – 1+2+3+4+5+6+7+8+9
Total set of numbers = 9 -1+1
Here , you can see that 9 is odd.
Next step is to find the middle number and the formula is
Smallest number + largest number / 2
So , for the above example ,
Smallest number – 1
Largest number- 9
So , middle number = 9+1 = 10. 10/2 = 5.
Ex. 2 – 9 , 10,11,12,13,14,15,16,17, 18,19
smallest number- 9
Largest number- 19
Total set of numbers = 19 – 9+1 = 11
Here, also 11 is an odd number
Middle number = 9+19= 28. 28/2 = 14
Now , last step is to multiply the middle number and the total set of numbers
Middle number × total set of numbers
14 × 11 = 154
So , the sum of 9 , 10,11,12,13,14,15,16,17,18,19 is
154
Isn’t it easy ?????
2. 2nd CASE – when the total set of numbers is even .
In this case , formula is same .
The difference is that here , middle number is a decimal number .
Ex – 84 , 85,86,87,88,89,90 ,91 ( trying with some bigger numbers )
Smallest number- 84
Largest number- 91
Total set of numbers is -. 91-84+1 = 8
Middle number =. 84+91= 175. 175/2 = 87.5
Here , the middle. Number is a decimal
But the technique is same .
Sum = middle number × total set of numbers
Sum = 87.5 × 8 = 875/10 × 8 [ you can cancel as well ( 10 = 5 × 2 , so 5 can be cancelled by 875 and 2 can be cancelled by 8 , see how === 875/ 5 = 175 and 8/2 = 4 and last step to multiply 175 × 4 = 700 ) ]
Or
You can just multiply
87.5 × 8 = 700
So , this 700 is the sum of 84+85+86+87+88+89+90+91 .
Now , its your turn to try and test your knowledge
Find the sum , middle number and total set of numbers of this question –
78 , 79 , 80 , 81 , 82
Any doubts , comment section is open ?.
Till then this is Saesha Kapoor signing off. ?♂️?♂️?♂️