Question

The sum of three numbers in A.P is 27 the product of first and last numbers is 65. Find the numbers

Answer 1

Answer:

it is 9

Step-by-step explanation:

Let the three numbers in AP be a - d,a ,a + d

a - d + a + a + d=27

3a = 27

a = 9

If they would be a, a+d, a+2d then

a+a+d+a+2d = 27

a+d=9

d=0

tn = a + ( n - 1) d

= 9 +(n -1) 0

= 9

Answer 2

Step-by-step explanation:

let the three numbers be a-d, a, a+d

Therefore, By 1st condition:

a-d+a+a+d=27

a+a+a=27

3a=27

a=27/3

a=9

by 2nd condition:

(a-d)×(a+d)=65

(a^2-d^2) =65

(9)^2 - d^2 = 65

81-d^2=65

81-65=d^2

d^2=16

d=√16

d=4

the 1st number= a-d = 9-4 =5

2nd number = a = 9

3rd number = a+d = 9 + 4 = 13

the no. s are 5,9,13