CBSE Class 11-science Answered
Show that the sum of n airhtmetic means between two numbers is n times the single A.M between them?
Asked by | 06 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 | 10 Aug, 2008, 05:07: PM
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