UPSC NDA Math Model Paper 10

Let the three numbers in A.P. be a – d, a, and a + d.
Given: the sum of three numbers in A.P. is 24
⇒ (a – d) + a + (a + d) = 24
⇒ 3a = 24
⇒ a = 8
Also, given: the product of three numbers in A.P. is 440.
⇒ (a – d) (a) (a + d) = 440
Put a = 8
⇒ (8 – d) (8) (8 + d) = 440
⇒ (8 – d) (8 + d) = 55
⇒64–d2=55
⇒d2=9
⇒d=±3
Therefore, when d = 3, the numbers are 5, 8, and 11 and when d = –3, the numbers are 11, 8, and 5.
So, the three numbers are 5, 8, and 11.