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The image displays a quiz asking to "solve for the missing terms in each item" with five sequences, each having multiple missing numbers. I'll help you solve each of the sequences:

1. **Sequence 1:** \(8, \_\_, \_\_, 64\)  
   This sequence might be based on powers of 2 or multiplication patterns. Let's explore:
   - \(8 = 2^3\)
   - \(64 = 2^6\)
   It could be a doubling pattern, so the sequence might be:  
   \(8 \times 2 = 16\),  
   \(16 \times 2 = 32\),  
   \(32 \times 2 = 64\)  
   Thus, the missing numbers are **16, 32**.

2. **Sequence 2:** \(3, \_\_, \_\_, \_\_, 144\)  
   A possible pattern here could be multiplication by a certain factor:
   - If we use the factor 2, it could be:  
   \(3 \times 2 = 6\),  
   \(6 \times 2 = 12\),  
   \(12 \times 2 = 24\),  
   \(24 \times 2 = 48\),  
   But this does not lead to 144, so another pattern might involve squares or more complex multiplications. Testing squares:
   - \(3^2 = 9\),  
   \(9^2 = 81\),  
   \(81^2 = 144\),  
   The pattern seems to work with powers, leading us to test the middle terms more. 

3. **Sequence 3:** \(80, \_\_, \_\_, 5/4\)  
   This could involve division by 2 or a fraction-based progression. Let's explore:
   - Starting from 80 and progressively halving:  
   \(80 / 2 = 40\),  
   \(40 / 2 = 20\),  
   To reach \(5/4\), we might introduce fractions:  
   \(20 / 2 = 10\),  
   \(10 / 2 = 5\), then \(5 / 4 = 1.25\)  
   The missing numbers could be: **40, 20, 10**.

4. **Sequence 4:** \(-16, \_\_, \_\_, \_\_, -1\)  
   Here, the numbers are negative, possibly following an arithmetic progression.  
   A common difference could be +5:
   - \(-16 + 5 = -11\),  
   \(-11 + 5 = -6\),  
   \(-6 + 5 = -1\).  
   So the missing numbers are **-11, -6**.

5. **Sequence 5:** \(6, \_\_, \_\_, \_\_, \_\_, 93570\)  
   This looks like a complex sequence, likely involving a rapid increase in size. Let's try to recognize a pattern. If it involves exponential growth or large multiplication steps, we need more details to find the exact terms.

Would you like a detailed explanation for any particular sequence? Here are five related questions to expand on the concept:

1. How do you identify patterns in arithmetic or geometric sequences?
2. What strategies can you use for recognizing complex number progressions?
3. How do powers of numbers help in predicting sequences?
4. What are common patterns in sequences involving fractions or divisions?
5. How can you handle sequences with both negative and positive numbers?

**Tip:** Always check if a sequence follows simple arithmetic (addition or subtraction) or geometric (multiplication or division) patterns before trying more complex operations.

Solve for the missing terms in each item. Show your solutions.
1. 8, __, __, 64
2. 3, __, __, __, 144
3. 80, __, __, 5/4
4. -16, __, __, __, -1
5. 6, __, __, __, __, 93570

Solve for the missing terms in sequences using arithmetic and geometric progression formulas. This guide includes step-by-step solutions and covers pattern recognition with fractions and negative numbers. Ideal for students in Grades 6-8.

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