Alternating Pattern
交替规律
Pattern / 模式识别What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Every other term behaves differently
- 2Two visual states alternate in a pattern
- 3Odd and even positions seem to follow different rules
What It Really Tests
The core mathematical idea behind this structure:
Two separate rules interleave — odd and even positions follow different patterns.
两套规则交替——奇数位和偶数位遵循不同的规律。
Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Forcing one single rule onto all terms
- ⚠Ignoring position parity (odd vs even index)
- ⚠Mixing the two layers together
Your First Step
How to begin thinking about problems with this structure:
Separate odd-position terms from even-position terms and check each sub-sequence.
把奇数位和偶数位的项分成两个子序列分别观察。
Try a Problem
A sequence begins: 3, 8, 5, 10, 7, 12, 9, ... What is the next number?
💡 Show Solution & Key Insight
Answer
C
Explanation
Odd-position terms: 3, 5, 7, 9 (increase by 2). Even-position terms: 8, 10, 12 (increase by 2). The next term is even-position, so 12 + 2 = 14.
Key Insight
Separate the sequence into two interleaved sub-sequences.
Common Wrong Path
Trying to find a single rule that governs all terms.
Related Structures
These structures share similar patterns or thinking approaches: