Show that the sum of n airhtmetic means between two numbers is n times the single A.M between them?

Asked by  | 6th Jul, 2008, 11:18: PM

Expert Answer:

let a and be be the two no.s

so one A.M. between them (b+a)/2

n times this mean  n* (b+a)/2

now if we have n A.M. between a and b then d=(b-a)/(n+1)

sum of these means by sum formula of arithmatic series =  n/2 (first term + last term)

here first term = a + (b-a)/(n+1)

last term = a + (n-1)*(b-a)/(n+1)

solving this we will get the same result as above .

Answered by  | 10th Aug, 2008, 05:07: PM

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