Pattern guide
Interleaved Sequences
Two independent sequences are woven together into one.
An Interleaved sequence hides two separate, simple sequences inside one. Terms at odd positions (1st, 3rd, 5th...) form one sequence, and terms at even positions (2nd, 4th, 6th...) form another. Once you split them, each half is usually straightforward.
How to recognise it
- 1Look at positions separately: write out terms 1, 3, 5... on one line and terms 2, 4, 6... on another.
- 2If each subgroup forms a simple arithmetic or geometric sequence, you have an Interleaved pattern.
- 3Longer sequences (7 or more terms) are a strong hint that interleaving is happening.
- 4A sawtooth shape (high, low, high, low) almost always indicates two interleaved sequences moving in opposite directions.
- 5The two sub-sequences often have different starting points and different rules.
Worked examples
Example 1
1
100
2
90
3
80
4
?
Rule: Odd positions: +1. Even positions: -10
Odd positions → 1, 2, 3, 4(each term adds 1)
Even positions → 100, 90, 80, ?(each term subtracts 10)
80 → ?(80 - 10 = 70)
Answer: Next even-position term: 80 - 10 = 70
Example 2
2
3
4
9
8
27
16
?
Rule: Odd positions: ×2. Even positions: ×3
Odd positions → 2, 4, 8, 16(each term ×2)
Even positions → 3, 9, 27, ?(each term ×3)
27 → ?(27 × 3 = 81)
Answer: Next even-position term: 27 × 3 = 81
Example 3
5
100
10
50
20
25
?
Rule: Odd positions: ×2. Even positions: ÷2
Odd positions → 5, 10, 20, ?(each term ×2)
Even positions → 100, 50, 25(each term ÷2)
20 → ?(20 × 2 = 40 (next odd position))
Answer: Next odd-position term: 20 × 2 = 40
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