The sum of three numbers in A.P. is 3 and their product is -35. Find the numbers.

Let the three numbers that are in A.P. be a - d, a, a + d.

Given, sum of three numbers = 3
⇒ a - d + a + a + d = 3
⇒ 3a = 3
⇒ a = 1.

Given, product of the numbers = -35
⇒ (a - d)(a)(a + d) = -35

Putting the value of a = 1 in the above eq we get,

⇒ (1 - d)(1)(1 + d) = -35
⇒ (1 - d²) = -35
⇒ d² = 1 + 35
⇒ d² = 36
⇒ d = $\sqrt{36}$
⇒ d = +6, -6.

∴ a - d = 1 - 6 = -5 or 1 - (-6) = 7 and a + d = 1 + 6 = 7 or 1 + (-6) = -5

Hence, the numbers are -5, 1, 7.