Question

Find the missing number in the series: \(2,\,6,\,12,\,20,\,30,\,?\)

• A. \(36\)
• B. \(40\)
• C. \(42\)
• D. \(44\)

Hint:

When solving number series, first check the differences between consecutive terms. Increasing differences often indicate an arithmetic pattern.

Answer 1

The Correct Option is C

Topic - Number Series:
This question requires identifying the mathematical pattern or progression in a given sequence of numbers.
Step 1: Understanding the Question:
Analyze the gap between consecutive numbers to find the rule governing the series.
Step 2: Key Formula or Approach:
Check for the difference between terms (Arithmetic progression or increasing difference).
Step 3: Detailed Solution:
1. Calculate the differences:
\(6 - 2 = 4\)
\(12 - 6 = 6\)
\(20 - 12 = 8\)
\(30 - 20 = 10\)
2. The differences are 4, 6, 8, 10. This is an AP with a common difference of 2.
3. The next difference should be \(10 + 2 = 12\).
4. The missing number is \(30 + 12 = 42\).
Step 4: Final Answer:
The next number in the series is 42.