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

Question

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

KnowledgeBoat · Accepted Answer

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 = ⇒ 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.

Mathematics

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

AP GP

Related Questions

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

If the numbers n - 2, 4n - 1 and 5n + 2 are in A.P., find the value of n.

The sum of three numbers in A.P. is 30 and the ratio of the first number to the third number is 3 : 7. Find the numbers.

The sum of the first three terms of an A.P. is 33. If the product of the first and the third terms exceeds the second term by 29, find the A.P.