Continue the pattern of increasing even increments: 2, 6, 12, 20, 30, 42, 56, ( … )

Introduction / Context:This additive series increases by consecutive even numbers. Recognizing the difference pattern is key to projecting the next term correctly.

Given Data / Assumptions:

• Series: 2, 6, 12, 20, 30, 42, 56, …
• Differences look like +4, +6, +8, +10, +12, +14.

Concept / Approach:List successive differences. If they are consecutive even numbers starting from 4, extend with the next even number to get the missing term.

Step-by-Step Solution:6 − 2 = 412 − 6 = 620 − 12 = 830 − 20 = 1042 − 30 = 1256 − 42 = 14Next difference = 16 ⇒ Next term = 56 + 16 = 72

Verification / Alternative check:Even-difference ladders are common: starting at 4 and adding 2 each step reproduces every jump perfectly, confirming 72.

Why Other Options Are Wrong:

• 60 / 64 / 70: imply differences of 4, 8, or 14 again; only +16 continues the rising-even pattern.

Common Pitfalls:

• Guessing the next term from a visual trend without calculating differences, which can be misleading.

Final Answer:72