Pattern guide
Taking Turns
Two different rules take turns. Odd positions follow one rule, even positions follow another.
A Taking Turns sequence applies two operations in rotation. Instead of one pattern running through all terms, you have two patterns interleaved: operation A on odd steps, operation B on even steps. The trick is recognising the alternation.
How to recognise it
- 1If the differences look inconsistent, check whether they alternate between two types.
- 2Look at every other step: does step 1→2 and step 3→4 do the same thing? Does step 2→3 and step 4→5 do the same thing?
- 3Common pairs: ×2 then -3, +5 then ×2, +odd then ×even.
- 4A common giveaway: the sequence alternates between going up by a lot and coming down a little (or vice versa).
- 5List the operations explicitly: ×2, -3, ×2, -3... and see if a two-step cycle emerges.
Worked examples
Example 1
4
8
5
10
6
12
7
?
Rule: Odd steps: +1. Even steps: ×2
4 → 8(×2 (even step))
8 → 5(+(-3)? No — let us re-read the pattern)
4 → 5(odd positions: 4, 5, 6, 7 — each +1)
8 → 10(even positions: 8, 10, 12 — each +2)
7 → ?(next is an even position: 12 + 2 = 14)
Answer: Next even-position term: 12 + 2 = 14
Example 2
10
20
17
34
31
62
?
Rule: Odd→even: ×2. Even→odd: -3
10 → 20(×2)
20 → 17(-3)
17 → 34(×2)
34 → 31(-3)
31 → 62(×2)
62 → ?(-3)
Answer: 62 - 3 = 59
Example 3
3
9
12
36
39
117
?
Rule: Odd→even: ×3. Even→odd: +3
3 → 9(×3)
9 → 12(+3)
12 → 36(×3)
36 → 39(+3)
39 → 117(×3)
117 → ?(+3)
Answer: 117 + 3 = 120
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