Question

Find the missing number in the series: 5, 11, 23, 47, ___

• A. 91
• B. 93
• C. 95
• D. 97

Hint:

You can also find the answer by tracking the differences between consecutive terms! The difference values are: $+6$, $+12$, and $+24$. Notice that the differences double each time. The next difference must be $24 \times 2 = +48$. Adding this to the last term gives: $47 + 48 = 95$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Number series puzzles require analyzing the operational relationships between adjacent numbers to discover a consistent mathematical progression. This specific sequence can be interpreted using a recursive rule involving multiplication and addition, or by examining the expanding differences between the terms.

Step 2: Key Formula or Approach:
Let's analyze the relationship pattern from term to term: $$\text{Term}_{n+1} = (\text{Term}_n \times 2) + 1$$ Alternatively, the difference sequence follows a power-of-two growth pattern: $$\text{Difference} = 6, 12, 24, 48, \dots$$

Step 3: Detailed Explanation:
Let's verify the $(\text{Previous Term} \times 2) + 1$ rule across the provided series elements: First to second term: $(5 \times 2) + 1 = 10 + 1 = 11$ Second to third term: $(11 \times 2) + 1 = 22 + 1 = 23$ Third to fourth term: $(23 \times 2) + 1 = 46 + 1 = 47$ Since the rule works perfectly for all terms, we apply this identical pattern to the final given number to find the missing value: \[ \text{Missing Term} = (47 \times 2) + 1 \] \[ \text{Missing Term} = 94 + 1 = 95 \]

Step 4: Final Answer:
The missing number in the series is 95.