Question

Find the missing term: 2, 6, 12, 20, 30, ?

• A. 36
• B. 40
• C. 42
• D. 44

Hint:

This specific series also follows the pattern $n^2 + n$.
$1^2+1=2, \ 2^2+2=6, \ 3^2+3=12, \ 4^2+4=20, \ 5^2+5=30$.
The next is $6^2+6=42$.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This is a number series problem where we look for a consistent pattern in the differences between consecutive terms.

Step 2: Key Formula or Approach:
The pattern follows an increasing difference: $d_n = d_{n-1} + 2$.

Step 3: Detailed Explanation:
Let's find the difference between each term:
• $6 - 2 = 4$
• $12 - 6 = 6$
• $20 - 12 = 8$
• $30 - 20 = 10$ The differences are $4, 6, 8, 10$. This is an arithmetic progression where each difference increases by 2. The next difference should be $10 + 2 = 12$. Adding this to the last term: \[ 30 + 12 = 42 \]

Step 4: Final Answer:
The missing term in the series is 42.