Question

The average of the squares of first 7 natural numbers is

Answer 1

the answer is the attachment

Answer 2

The average of square of first seven natural numbers is 20

Solution :  

Natural numbers are the numbers starting form 1, 2, 3,…. Infinity

The first seven natural numbers are 1, 2, 3, 4, 5, 6, 7

Square of first seven natural numbers are 1, 4, 9, 16, 25, 36, 49

Sum of the squares of first seven natural numbers are

1 + 4 + 9 +  16 +  25 +  36 +  49 = 140

Average of first seven natural numbers $\bold{=\frac{140}{7}=20}$.

By using average formula $\bold{=\frac{(n+1)(2 n+1)}{6}}$

n = 7 then,

Average of first seven natural numbers $=\frac{(7+1)(2(7)+1)}{6}$

$=\frac{120}{6}=20$.