Question 1 plz fast..../

Q1. If a , b, c are in AP and b , c, d be in HP, then 

       (a) ab = cd                    (b) ad = bc                        (c) ac = bd         

Dear Student,

The solution is as under:

since, a,b and c are in AP, thus,2b=a+c.....(i)     arithmetic meanand, b,c and d are in HP, thus,2c=1b+1d.....(ii)     harmonic meanor, 1b=2c-1dputting the value of b from (i), we get,2a+c=2c-1dor,2a+c=2d-cdcor, 2dc=a+c2d-cor, 2dc=2ad-ac+2dc-c2or, 2ad=c2+acor, 2ad=cc+afrom (i), as a+c=2bor, 2ad=c2bor, 2ad=2bcor, ad=bc

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