Question

Three numbers are in A.P. The product of the extremes is
5 times the mean, also the sum of the two largest is 8
times the least, the numbers are

Answer 1

Answer:

Given that

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

3a=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

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