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Question Number 101563 by harckinwunmy last updated on 03/Jul/20
Answered by bramlex last updated on 03/Jul/20
(2)1y+z,1z+x,1x+y→AP⇒2z+x=1y+z+1x+y2z+x=x+2y+z(y+z)(x+y)2(y2+yx+zx+zy)=(z+x)(x+2y+z)2y2+2yx+2zx+2zy=zx+2zy+z2+x2+2xy+xz2y2=x2+z2⇒sox2,y2,z2→AP
Answered by PRITHWISH SEN 2 last updated on 03/Jul/20
∵a,bandcarethethreecosecutivetermsofalinearsequence∴a+c=2bnowa(1b+1c)+c(1a+1b)=b(a2+c2)+ac(a+c)abc=b(a2+c2)+2abcabc=(a+c)2ac=2b(a+c)ac=2b(1a+1c)∴thetermsarealsothe3consecutivetermsofthesamelinearsequenceproved
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