Question

17. The mean of consecutive positive integers from 2 to n is

Answer 1

Mean = Sum of all terms / Number of terms

Terms start from 2 , 3....................... n

Number of terms is n - 1

Sum of terms is :

2+3+4+...........................n-1+n

This is an AP with a = 2

                              d = 1

                               n = n - 1

Sn is the sum of n terms

Sn of n terms is given as n / 2 [ 2 a + ( n - 1 ) d ]

Sn-1 of n - 1 terms  = ( n - 1 ) /2 [ 2×2 + ( n - 1 - 1 )(1)]

                             = ( n - 1 ) / 2 [ 4 + n - 2 ]

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

Mean = Sum of n-1 terms / n - 1

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

          = ( n + 2 ) / 2

That's it!

The mean will be ( n + 2 ) / 2

Hope it helps

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Answer 2

Answer:. (n+2)/2

Step-by-step explanation:

Ans = (sum of n terms - 1 )/ number of terms ..........

{subtracting 1 since question says mean of 2 to n terms }

Ans= 【 { [n (n+1) ] /2} -1 】/ (n-1)

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

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

=(n+2)/2