Question

Find the missing term: 3, 9, 27, 81, ___

• A. 162
• B. 189
• C. 243
• D. 324

Hint:

Memorizing the perfect exponent values for small bases like 2, 3, and 5 up to the 5th power is a great way to save time on number series questions!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Number series puzzles require identifying a consistent mathematical rule or pattern that links each consecutive term. This series forms a classic geometric progression, where each subsequent term is calculated by multiplying the previous term by a fixed number (the common ratio).

Step 2: Key Formula or Approach:
Examine the factor relationship between adjacent numbers: $$\text{Term}_2 = \text{Term}_1 \times r$$ $$\text{Term}_3 = \text{Term}_2 \times r$$ Once the common ratio ($r$) is found, apply it to the last given term to find the missing value.

Step 3: Detailed Explanation:
Let's check the ratio between each consecutive pair of numbers in the series: $3 \times 3 = 9$ $9 \times 3 = 27$ $27 \times 3 = 81$ The pattern shows that each number is multiplied by a common ratio of 3 to produce the next term. This can also be written as sequential powers of 3: $3^1 = 3$ $3^2 = 9$ $3^3 = 27$ $3^4 = 81$ Following this logic, the missing term must be $3^5$, or simply the previous term multiplied by 3: \[ \text{Missing Term} = 81 \times 3 = 243 \]

Step 4: Final Answer:
The missing term in the sequence is 243.