Question

if the mean of first 'n' natural numbers is 11 , then n=

Answer 1

Hello !
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Mean = sum of n natural numbers / n 
          = n(n+1) / 2n 
ATQ , 
n(n+1) / 2n = 11
n²+ n = 22n
n² - 22n + n = 0 
n² - 21 n = 0
n(n-21) = 0 
n = 0 
or n = 21 
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Answer 2

sum of n natural number :
Sn = 1 + 2 + 3 + 4 + 5 + 6 + 7 +........+ n
this is the form of an A.P
where a is equal to 1 , d = 1 and no of terms = n .
use, formula,
Sn = n/2 { 2a + ( n -1)d }
Sn = n/2 { 2 × 1 + ( n -1) × 1 }
Sn = n(n + 1)/2

hence,
sum of n of natural numbers = n( n +1)/2

mean = sum of natural numbers /total natural number .

mean = n(n +1)/2n
11 = (n +1)/2
22 = n +1
n = 21

hence , n = 21