Find three numbers in AP whose sum is 15 and product is 80.

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

Now, sum of the numbers = 15

∴ (a - d) + a + (a + d) = 15

⇒ 3a = 15

⇒ a = 5

Now, product of the numbers = 80

⇒ (a - d) × a × (a + d) = 80

⇒ a³ - ad² = 80

Put the value of a, we get,

125 - 5 d² = 80

⇒ 5 d² = 125 - 80 = 45

d² = 9

d = � 3

∴ If d = 3, then the numbers are 2, 5, 8.

If d = - 3, then the numbers are 8, 5, 2.