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There are n arithmetic means between 3 and 54 such that 8th mean is to the      (n-2)th mean = 3:5. Find n
Asked by rushabhjain.a | 20 Nov, 2018, 11:07: AM
8th mean = 9 th term in A.P = t9 = 3+8d
(n-2)th mean = (n-1)th term in A.P = t(n-1) = 3+(n-2)d

It is given that,  t9 / t(n-1) = 3/5  ;

If there are n arithmetic means between 3 and 54, then (n+2) terms are there in A.P.

hence, tn+2 = 3 +(n+1)d = 54  or (n+1)d = nd +d = 51 .......................(2)

By substituting nd from eqn.(1) in eqn(2), n is eliminated and we get d =3 . Hence n = 16
Answered by Thiyagarajan K | 22 Nov, 2018, 02:52: AM

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