Five numbers are in A . P . , whose sum is 25 and product is 2520 . If one of these five numbers is - 1 2 ,…

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
  1. 27
  2. 7
  3. 212
  4. 16

Solution

Let term be a-2d,a-d,a,a+d,a+2d
Sum =25⇒5a=25⇒a=5
Product =2520
5-2d5-d55+d5+2d=2520
⇒25-4d225-d2=504
⇒625-100d2-25d2+4d4=504
⇒4d4-125d2+625-504=0
⇒4d4-125d2+121=0
⇒4d4-121d2-4d2+121=0
⇒d2-14d2-121=0
⇒d=±1,d=∓112
d=±1, does not give -12 as a term
∴d=112
∴ Largest term =5+2d=5+11=16

Asked in: JEE Main 2020 (07 Jan Shift 1)

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