If a, b, c are in G.P. and logca, logbc, loga​b are in A.P. then find the common difference of the A.P.

dear student

let a,b,c be b/r,b,bra=b/rb=bc=brwhere r is the common ratio of GPnow the three terms are in AP2logcb= logac+logba2logclogb=logalogc+logbloga2logb+logrlogb=logb-logrlogb+logr+logblogb-logr2(1+t)=1-t1+t+11-t where t=logrbsimplifying we ge2t2+3t-3=0t21-t=32common difference=11-t-(1+t)=t21-t=32

regards

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