Question

The sum of three numbers in an AP is 18. If the product of the first and
the third term is 5 times
the common difference. Find the three numbers​

Answer 1

Answer:

the numbers are 2,6,10

Step-by-step explanation:

let the 1st term is a

common difference is d

so,2nd term is a+d

and,3 rd term is a+d+d=a+2d

according to question

a+(a+d)+(a+2d)=18

=> a+a+d+a+2d=18

=> 3a+3d=18

=> 3(a+d)=18

=> a+d=18/3=6

=> a=6-d

again,

a(a+2d)=5d

=> (6-d)(6-d+2d)=5d

=> (6-d)(6+d)=5d

=> 36-d^2=5d

=> d^2+5d-36=0

=> d^2+9d-4d-36=0

=> d(d+9)-4(d+9)=0

=> (d+9)(d-4)=0

=> d+9=0, d= -9

=> d-4=0, d=4

as the sum of the three numbers is positive,so d is positive.

here d=4

a=6-d=6-4=2

so the numbers are 2,2+4=6,6+4=10