Question

35. The mean of first 'n' odd natural numbers is n A. 2 n+1 B. 2 C.n D) n²

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Answer 1

Answer:

A. n

Step-by-step explanation:

We know the first n odd terms are in arithmetic progression with common difference (d) = 2, i.e. the difference between any two consecutive numbers is two.

We know, the first odd natural number (a) = 1

We know the nth odd natural number can be given as (an) = a + (n-1) d

Where a is the first term, n is the number of terms of the progression and d is the common difference.

= 1 + (n – 1) x 2

= 1 + 2n -1

= 2n -1

Where n belongs to the set of natural numbers = (1, 2, 3…)

We know, sum of first n terms in AP can be given as = n/2(a + an)

Therefore, sum of first n odd natural numbers

= n/2(1 + 2n - 1)

= n/2(2n)

= n²

We know Mean can be given as =

Sum of all terms ÷ Total number of terms

Mean of first n odd natural numbers =

Sum of first n odd natural numbers ÷ Total number of first n odd natural numbers

Mean of first n odd natural numbers = n²/n

⟹Mean of first n odd natural numbers = n

Hence, Mean of first n odd natural numbers is n. Option A is the correct answer.

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