Question:
What is the missing number in the following sequence? 3, 15, 35, 63, 99, __
What is the missing number in the following sequence? 3, 15, 35, 63, 99, __
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Numbers like 15, 35, 63, 99 are classic indicators of $(n^2 - 1)$.
Updated On: Jul 3, 2026
- 121
- 143
- 122
- 132
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The Correct Option is B
Solution and Explanation
Step 1: Concept
The sequence is composed of the products of consecutive even numbers or numbers that are one less than the squares of consecutive even integers.
Step 2: Meaning
Patterns: $2^2 - 1 = 3$; $4^2 - 1 = 15$; $6^2 - 1 = 35$; $8^2 - 1 = 63$; $10^2 - 1 = 99$.
Step 3: Analysis
The base numbers are $2, 4, 6, 8, 10$. The next even number is $12$.
Step 4: Conclusion
Calculation: $12^2 - 1 = 144 - 1 = 143$. Final Answer: (B)
The sequence is composed of the products of consecutive even numbers or numbers that are one less than the squares of consecutive even integers.
Step 2: Meaning
Patterns: $2^2 - 1 = 3$; $4^2 - 1 = 15$; $6^2 - 1 = 35$; $8^2 - 1 = 63$; $10^2 - 1 = 99$.
Step 3: Analysis
The base numbers are $2, 4, 6, 8, 10$. The next even number is $12$.
Step 4: Conclusion
Calculation: $12^2 - 1 = 144 - 1 = 143$. Final Answer: (B)
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