Question

If the mean the mean of first n natural numbers is 15. numbers of observations are​

Answer 1

The first n natural numbers are 1,2,3,...,n

Given that mean of n natural numbers is 15

⟹

n

1+2+3+...+n

=15 ———(1)

We know that sum of first n natural numbers is

2

n(n+1)

⟹1+2+3+...+n=

2

n(n+1)

———(2)

Substituting (2) in (1) we get

⟹

2n

n(n+1)

=15

⟹n+1=30⟹n=30−1=29

Answer 2

The correct option is (d) : 29

Given : MEAN of First n odd natural numbers is 15

First n natural numbers are : 1,2,3.........n  

MEAN = Sum of all the observations/ Total number of observations

MEAN = (1 + 2 + 3 + ……+ n )/n

MEAN = (n/2 (n + 1)) / n  

[The sum of the first n natural numbers : Sn = n/2 (a + l ) = n/2(1 + n) = n/2(n +1)]

15  = (n + 1) /2  

15 × 2 = n + 1

30 = n + 1

n = 30 - 1

n = 29

Hence, the value of n is 29 .  

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