Question

Look at this number series: 2, 6, 18, 54, ... What number should come next?

• A. 108
• B. 148
• C. 162
• D. 216

Hint:

When series terms grow very rapidly, test for multiplication (geometric progression) or exponential patterns (squares/cubes) before checking for simple addition.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a number series problem. We need to identify the mathematical pattern governing the sequence and calculate the next term.


Step 2: Key Formula or Approach:
Examine the ratio or difference between consecutive terms to determine if it is an arithmetic progression, geometric progression, or another pattern.


Step 3: Detailed Explanation:
Let's analyze the given series: \(2, 6, 18, 54\).
Calculate the ratio between consecutive terms:
\[ \frac{6}{2} = 3 \] \[ \frac{18}{6} = 3 \] \[ \frac{54}{18} = 3 \] The sequence is a geometric progression where each term is multiplied by a common ratio of 3 to get the next term.
To find the next term, multiply the last given term (54) by 3:
\[ 54 \times 3 = 162 \]

Step 4: Final Answer:
The correct choice is (C).