https://file.aiquickdraw.com/mathbot/file/1726067142866tpv7m5dc.jpg

Let's analyze the sequences shown in the image one by one:

1. **First sequence: 66, 44, 24, 6, ...**
   - The pattern is a decreasing sequence. 
   - Differences between terms: 
     - 66 - 44 = 22
     - 44 - 24 = 20
     - 24 - 6 = 18
   - The differences decrease by 2, so the next difference should be 16.
   - 6 - 16 = **-10**.
   - Next number: **-10**.

2. **Second sequence: 144, 12, 120, 10, ...**
   - Alternating pattern between a high and low number:
     - 144 → 120 (decreased by 24)
     - 12 → 10 (decreased by 2)
     - The alternating pattern suggests: 
       - The next number after 120 would decrease by 24: 120 - 24 = 96.
       - Next number: **96**.

3. **Third sequence: 22, 29, 43, 64, ...**
   - Differences between terms:
     - 29 - 22 = 7
     - 43 - 29 = 14
     - 64 - 43 = 21
   - The differences increase by 7 each time, so the next difference should be 28.
   - 64 + 28 = **92**.
   - Next number: **92**.

4. **Fourth sequence: 55, 74, 57, 72, 59, ...**
   - Alternating increases and decreases:
     - 55 → 74 (increased by 19)
     - 74 → 57 (decreased by 17)
     - 57 → 72 (increased by 15)
     - 72 → 59 (decreased by 13)
   - The pattern shows that the amounts of increase and decrease alternate between odd numbers (19, 17, 15, 13, ...).
   - The next change should be an increase by 11.
   - 59 + 11 = **70**.
   - Next number: **70**.

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Would you like further details or explanation on any of the sequences?

Here are five related questions you can explore:
1. Can you identify another sequence that follows a similar pattern to one of these?
2. How can you use differences between terms to predict the next number in a sequence?
3. What are other examples of alternating sequences similar to the second or fourth ones?
4. How would the patterns change if we modified the starting values of the sequences?
5. Can you design your own sequence with a decreasing difference pattern?

**Tip:** When analyzing sequences, pay attention to whether the differences between terms form their own pattern (e.g., increasing by a constant amount or alternating).

What comes next in each of the sequences: 66, 44, 24, 6,...; 144, 12, 120, 10,...; 22, 29, 43, 64,...; 55, 74, 57, 72, 59,...?

Learn how to solve missing terms in arithmetic and alternating sequences. Explore patterns like decreasing differences, alternating terms, and increasing intervals. Ideal for Grades 7-9.

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