Question

if a, b, c are in ap then prove that a(b+c)/bc, b(c+a)/ca and c(a+b)/ab are also in ap

Answer 1

If a,b,c are in AP then 2b=a+c
We have to prove
2(a+c)=(b+c)+(a+b)
so 2a+2c=2b+a+c
so a+c=2b
Which is true
Hence proved

Answer 2

u first takethe term individually u will get
a/c+a/b, b/a+b/c, c/b+c/a