Three numbers a,b,c are between 2 and 18 such that their sum is 25 and 2,a,b are A.P and b,c,18 are in G.P then abc  is

given that a+b+c=25 →1  since 2,a,b are in A.P ⇒2+b=2a−−−−2b,c,18 are in G⋅P⇒18b=c2−⋯−31 and 2, eliminate a ⇒3b+2c=48−−−−43 and 4⇒c2+12c=288→c=12,−24→c∈(2,18)⇒c=12,b=8,a=5→abc=480