1. Find the missing terms in each geometric sequence. Give the value of common ratio (r).

1. 3, 12, 48, _______, _________

2. _______, ________, 32, 64, 128

3. 120, 60, 30, ________, __________

4. 5, ________, 20, 40, _______

5. _____, 4, 12, 36,________,______

6. -2,________,______, -16, -32, -64

7. 256,________,________, -32, 16

8. 27, 9, ________,________1/3

9. 1/4,_______,________,_______,64, 256   

10. 5x², _________5x^6, 5x^8, __________    

Let's solve each geometric sequence one by one by first finding the common ratio \( r \) and then using it to find the missing terms.

### 1. \( 3, 12, 48, \_, \_ \)
- Common ratio \( r = \frac{12}{3} = 4 \)
- Next terms:
  - \( 48 \times 4 = 192 \)
  - \( 192 \times 4 = 768 \)

**Sequence:** \( 3, 12, 48, 192, 768 \)

### 2. \( \_, \_, 32, 64, 128 \)
- Common ratio \( r = \frac{64}{32} = 2 \)
- Previous terms:
  - \( 32 \div 2 = 16 \)
  - \( 16 \div 2 = 8 \)

**Sequence:** \( 8, 16, 32, 64, 128 \)

### 3. \( 120, 60, 30, \_, \_ \)
- Common ratio \( r = \frac{60}{120} = \frac{1}{2} \)
- Next terms:
  - \( 30 \times \frac{1}{2} = 15 \)
  - \( 15 \times \frac{1}{2} = 7.5 \)

**Sequence:** \( 120, 60, 30, 15, 7.5 \)

### 4. \( 5, \_, 20, 40, \_ \)
- Common ratio \( r = \frac{20}{5}

Find the missing terms in each geometric sequence. Give the value of common ratio (r).

Learn how to solve geometric sequences by finding the missing terms and calculating the common ratio (r). This guide covers the essential concepts of geometric sequences and provides step-by-step solutions for various examples. Suitable for students in Grades 8-10.

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