Question

What is the missing number in the following sequence? 2, 10, 26, 50, __, 122.

• A. 80
• B. 92
• C. 82
• D. 65

Hint:

When you see numbers near perfect squares (like 26, 50, 82), check for a $n^2 \pm 1$ pattern immediately.

Answer 1

The Correct Option is C

Step 1: Concept
The sequence follows a pattern based on the squares of consecutive even integers plus one.

Step 2: Meaning
We examine the relationship between the terms: $2 = 1^2 + 1$; $10 = 3^2 + 1$; $26 = 5^2 + 1$; $50 = 7^2 + 1$.

Step 3: Analysis
The sequence uses squares of odd numbers $1, 3, 5, 7$. The next odd number is $9$. Therefore, the missing term is $9^2 + 1 = 81 + 1 = 82$.

Step 4: Conclusion
Verifying with the final term: $11^2 + 1 = 121 + 1 = 122$. The pattern is consistent, making $82$ the correct answer. Final Answer: (C)