Geometric Progressions

Step 1: Recall the formula for the -th term of a GP.

The -th term of a GP is given by:

where is the first term, is the common ratio, and is the term number.

Step 2: Use the information about the 6th term to find .

The 6th term is given as , and the first term is . Using the formula for the -th term:

Substitute and :

Solve for :

Take the fifth root of both sides:

Note that and , so:

Step 3: Find the 5th term ( ).

The formula for the -th term is . For the 5th term:

Substitute and :

Compute :

Thus:

Final Answer: The 5th term of the GP is , which corresponds to option .