Question

I want a elegant method to solve this question i have already solved it though.

Answer 1

The sum of three numbers in an G.P is 70 , the two extremes be multiplied each by 4 and the mean by 5, the products are in A.P . Find the numbers

Answer 2

I am getting two values of "r" the common differnce

Answer 3

I need to see the original wording

Answer 4

wording? that is the exact question as from the textbook

Answer 5

the question is not clearly stated

Answer 6

let the final numbers in AP be
a-d,a,a+d
then
(a-d)/4 ,a/5 ,(a+d)/4 add upto 70

Answer 7

and these are in GP too

Answer 8

Well i considered
a/r , a , ar

Answer 9

so a/2 +a/5 =70
so
a= 100

Answer 10

but the mean of the GP is 20

Answer 11

a +ar + ar^2 =70r
a(1+r+r^2) =70r

From the second piece of information I got
4r^2 -10r +4 =0

and thus r = 1/2 and 2

Answer 12

I don't actually need extra large explanation and information , i will understand and percieve no problem

Answer 13

10, 20 and 40