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debadutta mishra Grade: 11
        

if (m+1)th,(n+1)th and (r+1)th terms of an A.P are in G.P,m,n&r are in H.P.then find the ratio of first term and common difference if this A.P.

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

Tm+1 = a + md


Tn+1 = a + nd


 Tr+1 = a + rd


Tm+1,Tn+1,Tr+1 are in gp therefore


(Tn+1)2  = (Tn+1)(Tr+1)


 (a+nd)2 = (a+md)(a+rd)


 (a/d +n)2 = (a/d + m)(a/d+ r)             ...............1


now   m,n,r are in hp therefore


 2/n =1/r + 1/m


 mr=n(m+r)/2.........2


let Z is the ratio of first term and common difference of AP then Z=a/d


putting Z in eq 1


 Z=mr - n2 /2n -(m+r) 


after putting value of mr from eq 2 we get


Z=a/d = -n/2


 


 


 


 

6 years ago
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