Question

Three numbers whose sum is 70 are in g.p. if each of the extremes is multiplied by 4 and the mean by 5,the numbers will be in a.p. find th e numbers

Answer 1

10 and 7.5 is your answer hope u like it

Answer 2

Answer:

10,20,40 or 40,20,10.

Step-by-step explanation:

Let the numbers be $a,ar,ar^2$ and sum = $70$.

$a(1+r+r^2)\;=\;70$ $\rightarrow(1)$

It is also given that $4a,5ar,4ar^2$ are in A.P.

$2(5ar)\;=\;4a+4ar^2\;=\;5r\;=\;2\;+\;2r^2$

$2r^2-5r+2\;=\;0$

$(2r-1)(r-2)\;=\;0$

$r\;=\;2,\frac{1}{2}$

Put r = 2 in (1), then a = 10.

Put r = $\frac{1}2} {$ in (1), then a = 40.

∴ The numbers are 10,20,40 or 40,20,10.