Question

The sum of the first 3 terms in AP is18. If the product first and the third terms is 5 times the common difference of AP find the 3 terms​

Answer 1

Answer:

[9/2, 9:40 PM] : The sum of 3 numbers in AP is 18. The product of the first and third number is 5 times the common difference

Let the first three numbers of A.P are (a-d), a and (a+d) where d is the common difference Sum of the first three numbers = (a-d) + a +(a+d) =

18 (given)

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

a-d + a +a+d = 18

За=18

a=6--(1)

Also, product of first and third term =5 times common difference

so the equation becomes

(a-d)(a+d) =5d

a²-d² = 5d

[9/2, 9:41 PM] : Substituting a=6 which we obtained from equation (1)

36-d² = 5d

= d² +5d -36=0

= d² +9d-4d-36=0

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

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

d=-9 and d=4

d=-9 is neglected

Hence d = 4

Three numbers are (a-d) + a +(a+d)= 2, 6, 10