Question

find the average of sum of square of first 10natural numbers​

Answer 1

TO FIND

The Average of Sum of Square of first 10 Natural Number.

SOLUTION

The First 10 Natural Numbers are 1,2,3,4,5,6,7,8,9 and 10.

Their squares are :-

1^2 = 1

2^2 = 4

3^2 = 9

4^2 = 16

5^2 = 25

6^2 = 36

7^2 = 49

8^2 = 64

9^2 = 81

10^2 = 100

Now, we shall find Average of all these Numbers :-

Average = Sum of All Numbers/Total No.

Average = (1+ 4+ 9+ 16 + 25+...+100)/10

= 385/10

= 38.5 (ANS)

ALTERNATE METHOD (Special Series)

* Given in the attachment.

Answer 2

Hello !!

For you answer this question, you only need make use of this method below. See the resolution.

The first 10 perfect squares.

1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 and 100.

Find the average of the first 10 perfect squares.

Average = (A1 + A2 + A3 ... + An)/n

Average = (1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100)/10

Average = (5 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100)/10

Average = (14 + 16 + 25 + 36 + 49 + 64 + 81 + 100)/10

Average = (30 + 25 + 36 + 49 + 64 + 81 + 100)/10

Average = (55 + 36 + 49 + 64 + 81 + 100)/10

Average = (91 + 49 + 64 + 81 + 100)/10

Average = (140 + 64 + 81 + 100)/10

Average = (204 + 81 + 100)/10

Average = (285 + 100)/10

Average = (385)/10

Average = 38.5

Final result : 38.5 is the average.

I hope I have collaborated !