Geometric Progression

Let the first term of the G.P. be and the common ratio be . The 2nd term is and the 5th term is . Given: Divide equation (2) by equation (1): So, the correct value of is . Wait! But this gives us option (4), not option (2). Let's double-check by solving precisely. Let’s verify: Given: 2nd term = 5th term = Divide: Confirmed again,

The correct option is (D):

Step 1: Understand what it means for to be in G.P.

If three numbers are in Geometric Progression, then:

Step 2: Cross-multiply the equation.

Step 3: Divide both sides by

Step 4: Hence, we get:

Step 1: Identify the first term and common ratio of the G.P.

First term,

Second term,

So, common ratio

Step 2: Use the formula for the term of a G.P.:

We are given , ,

Step 3: Set up the equation:

Now, express 729 as power of 3:

, so:

Equating powers of 3:

The correct option is (B):