Five numbers are in A . P . , whose sum is 25 and product is 2520 . If one of these five numbers is - 1 2 , then the greatest number amongst them is

Step-by-step solution

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