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CBSE Class 11-science Answered

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
answered-by-expert Expert Answer
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  ;
begin mathsize 12px style fraction numerator 3 space plus space 8 d over denominator 3 space plus space open parentheses n minus 2 close parentheses d end fraction space equals space 3 over 5 9 space plus space 3 n d space minus space 6 d space equals space 15 space plus space 40 d space 3 n d space equals space 46 d space plus space 6 space space space space o r space space space n d space equals space left parenthesis 46 divided by 3 right parenthesis d space plus space 2 space.................. left parenthesis 1 right parenthesis end style
 
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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