Five numbers are in A.P. whose sum is 25 and product is 2520, if one of these five numbers is −12 , then the greatest number amongst them is

Let terms be    a−2d,a−d,a,a+d,a+2d Sum = 25⇒5a=25⇒a=5  Also product = 2520     ⇒5−2d5−d55+d5+d=2520⇒25−4d225−d2=504⇒625−100d2−25d2+4d4=504⇒4d4−125d2+625−504=0⇒4d4−125d2+121=0⇒d2−14d2−121=0⇒d=±1,d=±112d=±1 is not possible since one of the terms is -12⇒d=112 ∴Largest term = 5+ 2d = 5 + 11 = 16