Find the next term in the sequence: 12, 15, 21, 30, 42, 57, __.

Introduction / Context:
We determine the rule generating the sequence. The increments between consecutive terms are increasing by a constant amount, a common pattern in aptitude tests.

Given Data / Assumptions:

• Sequence: 12, 15, 21, 30, 42, 57, __.

Concept / Approach:

• Compute consecutive differences and look for a simple pattern (e.g., +3, +6, +9 …).

Step-by-Step Solution:

Verification / Alternative check:
Continuing the +3 step keeps the structure consistent; 75 fits naturally as the next term.

Why Other Options Are Wrong:

• 59, 63, 65: Do not match the +3 ladder of differences.
• None of these: Not applicable; 75 is correct.

Common Pitfalls:

• Assuming constant difference or ratio instead of a second-level arithmetic pattern.

Final Answer:
75