Question

Choose the correct missing number: 3, 8, 15, 24, 35, ?

• A. 42
• B. 46
• C. 48
• D. 50

Hint:

Whenever the elements of a number sequence sit exactly one unit away from standard perfect squares ($4, 9, 16, 25, 36$), remember the Square $\pm$ Constant rule. Here, every single entry is exactly one less than a square ($n^2 - 1$). The next square is $49$, so your answer is $49 - 1 = 48$!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Number series puzzles require evaluating the progression behavior between consecutive numbers to discover a consistent mathematical pattern. This series can be decoded either by examining the expanding differences between adjacent terms or by mapping them to algebraic forms of perfect square integers.

Step 2: Key Formula or Approach:
Method 1 (Differences): Track the difference sequence $\text{Term}_{n+1} - \text{Term}_n$ to see if they follow an arithmetic layout. Method 2 (Square Pattern): Test if the terms align with the mathematical expression: $\text{Term}_n = n^2 - 1$.

Step 3: Detailed Explanation:
Let's analyze the arithmetic difference between each consecutive term: $8 - 3 = +5$ $15 - 8 = +7$ $24 - 15 = +9$ $35 - 24 = +11$ Notice that the differences are increasing consecutive odd numbers ($5, 7, 9, 11$). Following this exact mathematical behavior, the next difference added to the series must be the next odd number, which is $+13$. $$\text{Missing Number} = 35 + 13 = 48$$ Let's double check using the perfect square method ($\text{Square} - 1$): $2^2 - 1 = 4 - 1 = 3$ $3^2 - 1 = 9 - 1 = 8$ $4^2 - 1 = 16 - 1 = 15$ $5^2 - 1 = 25 - 1 = 24$ $6^2 - 1 = 36 - 1 = 35$ $7^2 - 1 = 49 - 1 = 48$ Both methods verify the exact same output.

Step 4: Final Answer:
The correct missing number is 48.