What is the arithmetic mean of first 16 natural numbers with weights being the number itself?

Options

A. `(17)/(2)`
B. `(33)/(2)`
C. 11
D. `(187)/(2)`

Answer

A

Explanation

Given natural numbers are
1, 2, 3, 4, 5, ………., 16
This is an A.P. with first term = 1
and common difference = 1, n = 16
`therefore" By using sum of 16 natural numbers"`
i.e., `S_(n)=(n)/(2)[2a+(n-1)d]`
We have
`s_(16)=(16)/(2)[2(1)+15(1)]=8(17)=136`
`thereforeAM.(136)/(16)=(17)/(2)`