If a,b,c∈(2,18), thena+b+c=25..(i)Since, 2,a,b are in AP.⇒2a=b+2 (ii)and b,c,18 are in GP.⇒c2=18b (iii)From Eqs. (i), (ii) and (iii),2b+2​+b+18b​=25⇒3b+2+62​b​=50⇒3b+62​b​−48=0⇒b+22​b​−16=0⇒b+42​b​−22​b​−16=0⇒b​(b​+42​)−22​(b​+42​)=0⇒(b​−22​)(b​+42​)=0⇒b=8,a=5 and c=12