Question

If 1/a+b,1/2b,1/c+b In AP. then prove a,b,c GP.​

Answer 1

Let b=ar and c=ar2. Then,

1a+b=1a+ar=1a(1+r),12b=12ar,and1(b+c)=1ar(1+r)

∴1(a+b)+1(b+c)=1a(1+r)=1ar(1+r)=(1+r)ar(1+r)=1ar=2×(12b).

Hence, 1(a+b),12b,1(b+c) are in AP.