Look at this number series: 2, 6, 18, 54, ... What number should come next?
Show Hint
When series terms grow very rapidly, test for multiplication (geometric progression) or exponential patterns (squares/cubes) before checking for simple addition.
Step 1: Understanding the Question:
This is a numerical sequence problem. Our objective is to discover the underlying mathematical rule and predict the subsequent number.
Step 2: Key Formula or Approach:
We should check the differences or ratios between adjacent terms to classify the sequence as arithmetic, geometric, or another specific pattern.
Step 3: Detailed Explanation:
Consider the provided sequence: \(2, 6, 18, 54\).
Let's find the ratio of each term to its predecessor:
\[ \frac{6}{2} = 3 \]
\[ \frac{18}{6} = 3 \]
\[ \frac{54}{18} = 3 \]
This confirms the sequence is a geometric progression with a constant common ratio of 3.
To obtain the next number, we simply multiply the final known term (54) by 3:
\[ 54 \times 3 = 162 \]
Step 4: Final Answer:
The correct choice is (C).