Math Problem Statement

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

  2. 3, 12, 48, _______, _________

  3. _______, ________, 32, 64, 128

  4. 120, 60, 30, ________, __________

  5. 5, ________, 20, 40, _______

  6. , 4, 12, 36,,___

  7. -2,____,__, -16, -32, -64

  8. 256,,, -32, 16

  9. 27, 9, ________,________1/3

  10. 1/4,,________,,64, 256

  11. 5x², _________5x^6, 5x^8, __________

Solution

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

1. 3,12,48,_,_3, 12, 48, \_, \_

  • Common ratio r=123=4r = \frac{12}{3} = 4
  • Next terms:
    • 48×4=19248 \times 4 = 192
    • 192×4=768192 \times 4 = 768

Sequence: 3,12,48,192,7683, 12, 48, 192, 768

2. _,_,32,64,128\_, \_, 32, 64, 128

  • Common ratio r=6432=2r = \frac{64}{32} = 2
  • Previous terms:
    • 32÷2=1632 \div 2 = 16
    • 16÷2=816 \div 2 = 8

Sequence: 8,16,32,64,1288, 16, 32, 64, 128

3. 120,60,30,_,_120, 60, 30, \_, \_

  • Common ratio r=60120=12r = \frac{60}{120} = \frac{1}{2}
  • Next terms:
    • 30×12=1530 \times \frac{1}{2} = 15
    • 15×12=7.515 \times \frac{1}{2} = 7.5

Sequence: 120,60,30,15,7.5120, 60, 30, 15, 7.5

4. 5,_,20,40,_5, \_, 20, 40, \_

  • Common ratio ( r = \frac{20}{5}

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Math Problem Analysis

Mathematical Concepts

Geometric Sequences
Ratios

Formulas

Common ratio formula: r = a_(n+1) / a_n

Theorems

Properties of geometric sequences

Suitable Grade Level

Grades 8-10