Skip to main content

average of first n natural numbers

By
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
                                 no of elements = 5
                                 average = 15/5 =3

by formula  = average of first 5 natural numbers = (n+1)/2 =(5+1)/2
                                                                                              =6/2
                                                                                              =3

Comments

Post a Comment

Popular posts from this blog

Average of first n even numbers

By
Even numbers are 2,4,6,8,10,…. Average = sum of elements/ no of elments Now we will see the sum of elements: Sum of first 2 even numbers: 2+4= 6= 2(2+1) Sum of first 3 even numbers: 2+4+6= 12= 3(3+1) Sum of first 4 even  numbers: 2+4+6+8=20= 4(4+1) Sum of first 5 even numbers: 2+4+6+8+10 = 30 = 5(5+1) Sum of first n even numbers: 2+4+6+8+10+. . . . .  n numbers= n(n+1) Now we will see average: Average of first 2 even numbers= (2+4)/2                                                           = 6/2                              ...
2 comments
Read more

product two consecutive odd numbers

By
Product of two consecutive odd numbers : Even numbers are 1,3,5,7,9,11,13,15,17,19,21,23,25,..... Odd  number means when we divide a number with 2,then the remainder is equal to one. Difference between the two odd numbers is 1. Now we will discuss the product of two odd  numbers. Now the product of two even numbers assumed to be 5x7 can be written as (6-1)x(6+1).                              5x7= (6-1)x(6+1) From the above we write general formula as 5x7= (6-1)x(6+1)=6 2 -1 2  =36-1=35 Now we can observe the result as one less than the square number. So now we can observe the following table. Column 1&2 reprecent the adjacent odd numbers. Column 3 represent the product of two adjacent odd numbers. Column 4 represent  the nearest square number. This  will arrive by adding 1 to the product  of two odd ...
Post a Comment
Read more

MULTIPLICATION OF TWO CONSECUTIVE NUMBERS

By
If you observe the sum of each digit in the Multiplication of two consectuive no.  pattern repeating:  2 6 3  2 3 6 2 9 9  n X n+1 Multiplication of two consectuive no. Sum of two digits 1X2 2 2 2X3 6 6 3X4 12 3 4X5 20 2 5X6 30 3 6X7 42 6 7X8 56 2 8X9 72 9 9X10 90 9 10X11 110 2 11X12 132 6 12X13 156 3 13X14 182 2 14X15 210 3 15X16 240 6 16X17 272 2 17X18 306 9 18X19 342 9 19X20 380 2 20X21 420 6 21X22 462 3 22X23 506 2 23X24 552 3 24X25 600 6 25X26 650 2 26X27 702 9 27X28 ...
Post a Comment
Read more