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.

Let the three numbers that are in A.P. be a - d, a, a + d. Given, sum of three numbers = 30 ⇒ a - d + a + a + d = 30 ⇒ 3a = 30 ⇒ a = 10. Given, the ratio of the first number to the third number = 3 : 7 Putting the value of a = 10 we get, ∴ a - d = 10 - 4 = 6 and a + d = 10 + 4 = 14. Hence, the numbers are 6, 10, 14.