Question

The sum of three numbers in Geomatric progression (GP) is 56. If we subtract 1,7,21 from three numbers in that order we obtain an Arithmatic Progression (AP), find these numbers?

Answer 1

consider them as a ar ar^2 add them for 56 then subtract respectively no.s now,
2(ar-7) = a-1+ ar^2-21 you have two equations and two variable solve it..

Answer 2

the sequence may be 8,16,32 or 32,16&8 both are the same you can also solve it by taking the terms as a/r, a, ar if you don't get it, i can upload a copy of my solution

Answer 3

please let me know that my answer is right or not

Answer 4

please upload ur copy solution @rajat97

Answer 5

the files are not getting attached so i'll give you a hint and i'll try to post a reply with my solution by evening
so first of all assume the numbers to be a/r, a, ar(a=first term, r=common ratio)
so, by the given condition, we get a/r+a+ar=56
by taking lcm, we get, (a+ar+ar^2)/r=56(therefore, (a+ar^2)/r+a=56 -equation 1)
then according to the second condition, we get 2a+8=(a+ar^2)/r
we put (a+ar^2)/r=2a+8 in equation 1.
we get 3a=48 and a=16
now put the value of a=16 in (a+ar+ar^2)/r=56
after substituting a with 16, we get the qudratic equation 16r^2-40r+16=0
this equation gets reduced to 2r^2-5r+2=0
thus the values of r come out to be 2 or 1/2
now put the values of r and a in the individual numbers i.e. a/r, a, ar
so we get the gp 8, 16, 32(if you take r=2) or 32, 16, 8(if you take r=1/2).
if you don't get any of these steps, feel free to ask anything