In the following question, a decreasing number series based on powers of 3 is given. Select the missing number from the series: 2187, 729, 243, 81, 27, ?

Introduction / Context:
This series 2187, 729, 243, 81, 27, ? is clearly built from powers of 3. Such questions check recognition of exponential patterns and division by a constant factor between consecutive terms. It is common in reasoning and quantitative sections to test familiarity with basic powers like 3^7, 3^6, and so on.

Given Data / Assumptions:

• Series: 2187, 729, 243, 81, 27, ?
• Options: 10, 9, 13, 11.
• We assume that the pattern of dividing by a constant continues consistently.

Concept / Approach:
We identify each term as a power of 3 and then see how the exponent changes. If the exponent decreases in a steady way, the next term is just the next lower power of 3. This is much faster than working on raw division alone, though both views lead to the same answer.

Step-by-Step Solution:
Step 1: Express each term as a power of 3.2187 = 3^7.729 = 3^6.243 = 3^5.81 = 3^4.27 = 3^3.Step 2: Observe the pattern.The exponent decreases by 1 at each step: 7, 6, 5, 4, 3, so the next exponent should be 2.Step 3: Compute the next power.3^2 = 9.Step 4: Alternatively, check via division.2187 / 3 = 729, 729 / 3 = 243, 243 / 3 = 81, 81 / 3 = 27, so the next term is 27 / 3 = 9.

Verification / Alternative check:
Using both the exponent view and the division view, we get the same result. Listing the sequence including the missing term gives 2187, 729, 243, 81, 27, 9, which corresponds to 3^7, 3^6, 3^5, 3^4, 3^3, 3^2. No contradictions appear at any step.

Why Other Options Are Wrong:
10: Is not a power of 3 and does not equal 27 divided by 3.13: Also does not match 3 raised to any small integer exponent in this context.11: Again is unrelated to the clear pattern of powers of 3 and simple division by 3.

Common Pitfalls:
Sometimes candidates attempt to find mixed additive and multiplicative patterns even when a very simple exponential relation is present. Memorising small powers of 2, 3, 5, and 7 is extremely useful, since many exam series questions are based on these. Recognising 2187 as 3^7 quickly unlocks the entire pattern here.

Final Answer:
The missing term, obtained either as 3^2 or as 27 divided by 3, is 9.