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average of first 100 odd numbers

Odd numbers are 1,3,5,7,9,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 odd numbers: 1+3= 4= 2 2 Sum of first 3 odd numbers: 1+3+5= 9= 3 2 Sum of first 4 odd numbers: 1+3+5+7=16= 4 2 Sum of first 5 odd numbers: 1+3+5+7+9 = 25 = 5 2 Sum of first n odd numbers: 1+3+5+7+9+. . . . . n numbers= n 2 Now we will see average: Average of first 2 odd numbers= (1+3)/2 = 4/2 =2 Average of first 3 odd numbers= (1+3+5)/3 = 9/3 =3 Average of first 4 odd numbers= (1+3+5+7)/4 = 16/4 =4 Average of first 5 odd numbers= (1+3+5+7+9)/5

LOGIC BEHIND MAGIC SQUARE

Assume a magic square of 3x3 A B C D E F G H I The above figure shows a 3x3 magic square. In the magic square sum of colum, row, diagnol numbers should be same A+B+C=D+E+F=G+H+I=A+D+G=B+E+H=C+F+I=A+E+I=C+E+G=sum A+B+C D+E+F G+H+I A+D+G B+E+H C+F+I A+E+I C+E+G By seeing the above there is 8 type of sum is available. Row wise-3, column wise-3, diagnol wise-2. Condition#1: There are 8 different combinations are there with same sum in a magic square. In the above 8 combinations A=2 times, B= 3 times, C= 2 times, D=3 times E=4 times, F=3 times, G=2 times, H=3 times, I= 2 times Hence the above forms the condition#2. In simply condition#2, middle number E appears 4 times in 8 combinations. Hence row, column, diagnol sum should be equal. In 3x3 magic square we are taking numbers from 1 to 9. From 9 numbers we need to take 3 numbers. From combination f

average of first n natural numbers

The natural numbers are 1,2,3,4,5,. . . . . . now we will see the sum of natural numbers sum of first 3 natural numbers= 1+2+3=6 the above can be written as sum of first 3 natural numbers= 1+2+3=6=3(3+1)/2 sum of first 4 natural numbers= 1+2+3+4=4(4+1)/2 then sum of n natural numbers=1+2+3+......n terms=n(n+1)/2 then the average formula = sum of elements/no of elements the average of n natural numbers= sum of elements/ no of elements =(n(n+1)/2)/n =n(n+1)/2xn =(n+1)/2 THE AVERAGE OF FIRST N NATURAL NUMBERS=(n+1)/2 The average of first 5 natural numbers sum of 5 natural numbers=1+2+3+4+5=15

Arithmetic1

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