Math Problem Statement
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Find the missing terms in each geometric sequence. Give the value of common ratio (r).
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3, 12, 48, _______, _________
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_______, ________, 32, 64, 128
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120, 60, 30, ________, __________
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5, ________, 20, 40, _______
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, 4, 12, 36,,___
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-2,____,__, -16, -32, -64
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256,,, -32, 16
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27, 9, ________,________1/3
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1/4,,________,,64, 256
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5x², _________5x^6, 5x^8, __________
Solution
Let's solve each geometric sequence one by one by first finding the common ratio and then using it to find the missing terms.
1.
- Common ratio
- Next terms:
Sequence:
2.
- Common ratio
- Previous terms:
Sequence:
3.
- Common ratio
- Next terms:
Sequence:
4.
- 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
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