the sum of 4 numbers in a.p is 40 and the product of their extremes is 91.the number are

Let the numbers be (a - 3d), (a - d), (a + d), (a + 3d). Then,

Sum =  (a - 3d) + (a - d) + (a + d) + (a + 3d) = 40

⇒ 4a = 40

⇒ a = 10

Given, product of extremes = 91

⇒ (a - 3d)(a + 3d) = 91

⇒ a² - 9d² = 91

⇒ (10)² - 9d² = 91

⇒  - 9d² = 91 -100 = -9

⇒  d² = 1

⇒  d  = ±1

Case1: When a = 10 and d = 1, then numbers are:

10 - 3, 10 - 1, 10 + 1, 10 + 3

or 7,9,11,13

Case2: When a = 10 and d = -1, then numbers are:

10 + 3, 10 + 1, 10 - 1, 10 - 3

or 13, 11, 9, 7