Grade 9Algebra
prove that the sum of n arithmetic means between two numbers is n times single AM between them
prove that the sum of n arithmetic means between two numbers is n times single AM between them
1 Answer
Arun
Dear Priya
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)
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