Question

the product of three G. M. s between 4 and 1/4 is 1 . (true or false) ​

Answer 1

Answer: True

Step-by-step explanation:

Let three Geometric Mean are $G_{1}$,$G_{2}$,$G_{3}$

So ,

4, $G_{1}$, $G_{2}$,$G_{3}$ , $\frac{1}{4}$

Here , First Term a = 4

$5^{th}$ term = $\frac{1}{4}$

a$r^{4}$ = $\frac{1}{4}$

$r^{4}$ = $\frac{1}{16}$

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

Product of three G.M. are = $G_{1} G_{2} G_{3} = (ar)(ar^{2})(ar^{3})$$=a^{3}r^{6}$$=\frac{64}{64}$=1