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What is the constant ratio between consecutive terms in the following sequences: g) 7 1/2; 8; 8 1/2; 9; ... h) 3.05 mm; 3.1 mm; 3.15 mm; 3.2 mm; ...?

Mathematics

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here are the solutions for the remaining questions:

.1

2. What is the constant ratio between the consecutive terms?

  • g) 7127\frac{1}{2}; 8; 8128\frac{1}{2}; 9; ...
  1. Calculate the ratio between consecutive terms.

    $\frac{8}{7.5} = \frac{16}{15}$  
    $\frac{8.5}{8} = \frac{17}{16}$
    
  2. Compare the ratios.

    Since $\frac{16}{15} \neq \frac{17}{16}$, there is no constant ratio. This is an arithmetic sequence with a constant difference of 0.5.  
    There is $\boxed{\text{no constant ratio}}$.
    
    • h) 3,05 mm; 3,1 mm; 3,15 mm; 3,2 mm; ...
  3. Calculate the ratio between consecutive terms.

    $\frac{3.1}{3.05} \approx 1.01639$  
    $\frac{3.15}{3.1} \approx 1.01613$
    
  4. Compare the ratios.

    Since $1.01639 \neq 1.01613$, there is no constant ratio. This is an arithmetic sequence with a constant
    
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