Fifth term of G.P is 2 The product of its first nine terms is

The correct answer is: 512

 Detailed Solution
Given that
 term of a G.P. is 2
Let first term as a and the r be the common ratio of the whole G.P.

Then fifth term will be 
But we are asked to find the product of 9 terms of the G.P.

So we can write the product as  
So ,

 

 

Now we can write the terms with base a separately and those with r separately.

 

 

 

Now adding the powers of the bases separately,

 

 

But we have to write this in the form of power 4,

 

Now we will take the common power out,

 

Putting the value of fifth term in above bracket,

 

 

 

 

Thus, the product of its first nine terms is 512.

 

Here note that the fifth term is having fourth power of 2 and not fifth power. We need not to find all nine terms separately; only finding the product is enough because that product will then be written in the form of the term that is known. Terms in a G.P. are having a common ratio in between. That’s why the power of r is increasing as the terms are increasing.