Question

If 5 gms introduced between 486 and 2/3, then 4th Gm is

Answer 1

Answer:

The 4th term of GM is 18.

Step-by-step explanation:

Given : If 5 GM introduced between 486 and 2/3.

To find : The 4th GM ?

Solution :

If the numbers have a GM then they are in a GP.

So the numbers will be $486, 486r, 486r^2, 486r^3, 486r^4, 486r^5, \frac{2}{3}$

The first term is a=486.

According to the series,

$486r^6=\frac{2}{3}$

$r^6=\frac{1}{729}$

$r=\frac{1}{3}$

The common ratio is $r=\frac{1}{3}$

So, the numbers are

$a_1=486$

$a_2=486\times \frac{1}{3}=162$

$a_3=486\times \frac{1}{9}=54$

$a_4=486\times \frac{1}{27}=18$

$a_5=486\times \frac{1}{81}=6$

$a_6=486\times \frac{1}{243}=2$

$a_7=\frac{2}{3}$

Therefore, The 4th term of GM is 18.