Question

Three numbers are in A.P their sum is 18 and their product is 162. Find the numbers.

Answer 1

The three numbers are 3,6,9

Answer 2

Given:

Three numbers are in A.P their sum is 18 and their product is 162.

To Find:

Find the three numbers?

Solution:

Let three number in A.P series are:

(a-d) , a , (a+d)

Given that sum of three number is 18:

(a-d) + a +(a+d) = 18

⇒a-d + a + a+d = 18

⇒3 a = 18

∴ a = 6     ...1)

Given that product of three number is 162:

(a-d) × a × (a+d) = 162

⇒(6-d) × 6 × (6+d) = 162

⇒(6-d)  × (6+d) = 27

⇒6² - d² = 27

⇒ - d² = 27 - 6²

⇒- d² = 27 - 36

⇒ - d² = -9

⇒d² = 9

∴ d = ± 3    ...2)

If d = 3, then:

First number = a-d = 6 - 3 =3

Second number = a = 6

Third number = a + d = 6 + 3 = 9

If d = -3, then:

First number = a-d = 6 + 3 =9

Second number = a = 6

Third number = a + d = 6 -3 = 3

From above we see that three number are:

3 , 6 and 9