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If `a , b , c`are in A.P. `b , c , d`are in G.P. and `1/c ,1/d ,1/e`are in A.P. prove that `a , c , e`are in G.P.?A. a,c,e are in G.P.B. a,b,e are in G.P.C. a,b,e are in G.P.D. a,c,e are in G.P.

Answer» Correct Answer - A
It si given that :
a,b,c are in A.P. `rArr2b=a+c` . . .(i)
b,c,d are in G.P. `rArrc^(2)=bd` . . .(ii)
`(1)/(c),(1)/(d),(1)/(e)` are in A.P. `rArr(2)/(d)=(1)/(c)+(1)/(e)rArrd=(2ce)/(c+e)` . . .(iii)
From (ii) and (iii), we obtain
`c^(2)=b((2ce)/(c+e))" [On eliminating d]"`
`rArr" "2be=c^(2)+ce`
`rArr" "(a+c)e=c^(2)+ce`
`rArr" "c^(2)=ae" [Using (i)]`
`rArr" "a,c,e,` are in G.P.


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