Question

1/a , 1/b and 1/c Are in A.P. show that: bc, ca and ab are also in ap

Answer 1

If same number is multiplied to numbers of a sequence in AP, the resulting sequence of numbers are also in AP.
$\frac{1}{a} \: \: \: \: \: \frac{1}{b} \: \: \: \: \: \frac{1}{c} \: \: are \: in \: ap \\ multiplying \: \: by \: \: \: abc \\ \frac{abc}{a} \: \: \: \: \: \frac{abc}{b} \: \: \: \: \: \frac{abc}{c} \: \: are \: \: also \: in \: ap \\ bc \: \: \: \: \: ca \: \: \: \: \: ab \: \: are \: \: in \: \: ap$