https://file.aiquickdraw.com/mathbot/file/1724732158187n7kiwnkd.jpg

Test lI. ldentify the next term in the pattern.
1. ABA, CDC, EFE, GHG, ___
2. 12, 13, 15, 18, 22,__
3. 7, 20, 47, 94, 167, ___
4. 1,4, 2, 8, 6, 24, 22,____
5. 11, 23, 48, 99, _____HH
6.6, 13, 27, 55, 111, ___
7. 8, -24, 72, -216, 648, -1944,____
8. R2BC, S3DE, T4FG, _____
9. 34, 7, 37, 14, 40, 28, ___
10. 16384, 8192, 2048, 256, 16, ______

The image should be like to show the solution

To solve the patterns in the provided image, I'll analyze each sequence individually:

1. **ABA, CDC, EFE, GHG, ___**  
   The pattern follows an increasing alphabetical sequence for both the first and third letters, while the middle letter remains constant and progresses alphabetically.
   - A, C, E, G → The next letter in sequence is I.
   - B, D, F, H → The next letter is J.
   - The third letter is a repetition of the first.
   **Answer: IJI**

2. **12, 13, 15, 18, 22, __**  
   The pattern appears to be increasing by sequentially larger increments.
   - 12 → 13 (+1)
   - 13 → 15 (+2)
   - 15 → 18 (+3)
   - 18 → 22 (+4)
   - The next increment should be +5.
   **Answer: 27**

3. **7, 20, 47, 94, 167, ___**  
   The pattern seems to be adding sequentially larger odd numbers to each term.
   - 7 → 20 (+13)
   - 20 → 47 (+27)
   - 47 → 94 (+47)
   - 94 → 167 (+73)
   - The next increment is 73 + 28 (as it follows an increment of 14, 20, 26, 28 in increments).
   **Answer: 270**

4. **1, 4, 2, 8, 6, 24, 22, ____**  
   The sequence alternates between multiplication by 4 and subtraction of 2.
   - 1 → 4 (×4)
   - 4 → 2 (−2)
   - 2 → 8 (×4)
   - 8 → 6 (−2)
   - 6 → 24 (×4)
   - 24 → 22 (−2)
   - The next step should be multiplication by 4.
   **Answer: 88**

5. **11, 23, 48, 99, ____**  
   The pattern increases by successively larger numbers, which seem to follow a specific pattern.
   - 11 → 23 (+12)
   - 23 → 48 (+25)
   - 48 → 99 (+51)
   - The increments double each time, so the next increase should be 102.
   **Answer: 201**

6. **6, 13, 27, 55, 111, ____**  
   The sequence follows a pattern of doubling and subtracting one.
   - 6 → 13 (×2 + 1)
   - 13 → 27 (×2 + 1)
   - 27 → 55 (×2 + 1)
   - 55 → 111 (×2 + 1)
   - The next step follows the same pattern.
   **Answer: 223**

7. **8, -24, 72, -216, 648, -1944, ____**  
   This is a geometric sequence where each term is multiplied by -3.
   - 8 × (-3) = -24
   - -24 × (-3) = 72
   - 72 × (-3) = -216
   - -216 × (-3) = 648
   - 648 × (-3) = -1944
   - -1944 × (-3) = 5832
   **Answer: 5832**

8. **R2BC, S3DE, T4FG, ____**  
   The pattern involves an increment in both the letter and the number.
   - R → S → T → U
   - 2 → 3 → 4 → 5
   - BC → DE → FG → HI
   **Answer: U5HI**

9. **34, 7, 37, 14, 40, 28, ____**  
   This sequence seems to alternate between adding 3 and subtracting 27.
   - 34 → 7 (−27)
   - 7 → 37 (+30)
   - 37 → 14 (−23)
   - 14 → 40 (+26)
   - 40 → 28 (−12)
   - Next, it would add 3.
   **Answer: 31**

10. **16384, 8192, 2048, 256, 16, ____**  
    The sequence divides by 2, 4, 8, 16.
    - 16384 ÷ 2 = 8192
    - 8192 ÷ 4 = 2048
    - 2048 ÷ 8 = 256
    - 256 ÷ 16 = 16
    - 16 ÷ 32 = 0.5
    **Answer: 0.5**

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Here are 5 questions related to this topic:
1. How do arithmetic sequences differ from geometric sequences?
2. What is the general formula for the nth term of an arithmetic sequence?
3. How can you determine the common difference in a sequence?
4. What strategies can you use to identify patterns in non-linear sequences?
5. How do alternating sequences influence the pattern recognition process?

**Tip:** When analyzing number sequences, pay close attention to the differences between terms, as they often provide clues to the underlying pattern.

Explore solutions to complex number pattern problems with detailed explanations and examples. This guide covers various patterns including arithmetic and geometric sequences. Suitable for Grades 7-9 students and those interested in mathematical problem-solving.

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