Number series (increasing differences by 2): 2, 6, 12, 20, 30, 42, 56, (…) Determine the next term by analyzing the second-order pattern in differences.

Introduction / Context:
This sequence grows faster than linear, suggesting a pattern in the differences. Many aptitude series increase the gap between terms by a constant increment (here, by 2).

Given Data / Assumptions:

• Terms: 2, 6, 12, 20, 30, 42, 56, (…)
• We consider first differences to detect a secondary pattern.

Concept / Approach:
Compute consecutive differences and inspect whether those differences follow a simple rule (e.g., arithmetic progression). If the differences increase by 2 each time, we can extrapolate the next difference.

Step-by-Step Solution:

Verification / Alternative check:
Check the pattern against earlier terms: each step adds consecutive even numbers starting from 4; this holds throughout.

Why Other Options Are Wrong:

• 61, 64, 70: Do not match adding 16 to 56; they would imply incorrect next differences.

Common Pitfalls:
Assuming multiplication when addition with changing differences is used. Always examine differences before products or ratios.

Final Answer:
72