Question

If a ,b, c are in A. P then k^a ,k^, b k^c are in G.P is he correct justify?

Answer 1

we know that b=a+c/2 becauce a,b,c are in ap we know that b=(ab)^1/2 . we should prove k^a,k^b,k^c are in gp. proof : k^b = k^a+c/2 then k^b=(k^a(k^b))^1/2. hence k^a, k^b,k^c are in gp