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Grade: 9
        
prove that the sum of n arithmetic means between two numbers is n times single AM between them
 
one year ago

Answers : (1)

Arun
17659 Points
							
Dear Priya
 
Let n a.m, between a,b are a1,a2,a3,............an
a,a1,a2,a3,.............an,b
sum of n a.m.
Sn = n[2a1 + (n-1)d]/2 ----------(1)
a.m. of a,b is (a+b)/2
b = a+(n+1)d
a.m. = [2a+(n+1)d]/2 -------------(2)
a1 = a+d put in (1)
Sn = n[2a + 2d + (n-1)d]/2
    = n[2a+(n+1)d]/2   ------------(3)
from equation (2) & (3) 
Sn = n*a.m.
where d = common difference of a.p.
 
Regards
Arun (askIITians forum expert)
one year ago
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