Question

The sum of three consecutive numbers in A.P is 27 and their products is 585 find the Numbers

Answer 1

Answer: The numbers are 5, 9, and 13.

Step-by-step explanation:

Let three consecutive numbers in A.P. be a-d, a, and a+d.

The sum of these three numbers= (a-d) + a + (a+d)= 3a

3a= 27 (given)

=> a= 9

The product of these three numbers= (a-d)a(a+d)= a(a^2-d^2)

a(a^2-d^2)= 585

Plugging the value of a in the above equation, we get

9(9^2-d^2)= 585

9^2-d^2= 585/9= 65

81 - d^2= 65

d^2= 81 - 65 = 16

Taking square root both sides, we get

d= 4, -4

Here, we take only positive number, as negative number does not satisfy the given conditions.

So,

d= 4

Now, the three consecutive numbers would be as follow:

a-d= 9-4= 5

a= 9

a+d= 9+4= 13

Answer 2

Answer:

Yes explain it by the three consecutive numeers are

Step-by-step explanation:(a-d)+a+(a+d) and then step by step