If abc≠0and the system of equationsx+7ay+2az=0,x+6by+2bz=0,  x+5cy+2cz=0  has a non – trivial solution, Then a,b,c are in

Since the given system has non-trivial solution, Δ=0 ⇒17a2a16b2b15c2c=0⇒1(12bc−10bc)−7a(2c−2b)+2a(5c−6b)=0⇒2bc−4ac+2ab=0⇒2ac=ab+bc⇒2b=1c+1a ⇒a,b,care in H.P