Question 8 Exercise 4.2

Solutions of Question 8 of Exercise 4.2 of Unit 04: Sequence and Series. This is unit of A Textbook of Mathematics for Grade XI is published by Khyber Pakhtunkhwa Textbook Board (KPTB or KPTBB) Peshawar, Pakistan.

If b+caa,c+abb,a+bcc are in A.P, then prove 1a,1b,1c are in A.P. GOOD

Since b+caa,c+abb,a+bcc are in A.P, thus
c+abbb+caa=a+bccc+abbLetS=a+b+c2a+b+c=2Sthena+bc=2(Sc)a+cb=2(Sb),andb+ca=2(Sa) then (1), becomes
2(Sb)b2(Sa)a=2(Sc)c2(Sb)b Dividing both sides by 2
SbbSaa=SccSbba(Sb)b(Sa)ab=b(Sc)c(Sb)bcaSabbS+abab=bSbccS+bcbc(ab)Sab=(bc)Sbc Dividing both sides by S
abab=bcbcaabbab=bbccbc1b1a=1c1b1a,1b,1c are in A.P.