Find four geometric means between 25 and 800.

Question

asked Dec 24, 2019 203k views

1 Answer

Erik Porter · Answer 1 · 2019-12-29T12:32:37+0000

Actually, you have to find four missed terms of geometrical sequence. Denote

$a_1=25,\\ a_6=800$

and r - ratio, then

$a_2=a_1\cdot r=25r,\\a_3=a_1\cdot r^2=25r^2,\\a_4=a_1\cdot r^3=25r^3,\\a_5=a_1\cdot r^4=25r^4,\\a_6=a_1\cdot r^5=25r^5$ .

Since
a_6=800 , you have that
800=25r^5 , then

$r^5=(800)/(25) =32,\\r=2$ .

Now substitude r=2 in each of unknown 4 terms:

$a_2=25\cdot 2=50,\\a_3=25\cdot 2^2=100,\\a_4=25\cdot 2^3=200,\\a_5=25\cdot 2^4=400$ .

Answer: four geometric means between 25 and 800 are 50, 100, 200, 400.